Once you know what a Plain and a Purl are, pick a small shuttle. You should be able to put all four fingers on it at once, but it needn't be any larger than that; it must be narrow enough to pass easily between two of your fingers.
It is easy to ruin a shuttle by winding it too tight or too full, by leaving it wound for too long, or by winding it with too coarse a thread, so if you have a fine antique shuttle, put it into a glass box and admire it until you've spoiled enough cheap shuttles to know what causes trouble. Get your first shuttle at a discount store or artsy-craftsy shop; it's actually better if it's made of poor material that's easy to damage: it will teach you what constitutes being careful.
Choose a bright or dark color of fine thread -- #70 at the thickest. The color should show up well against paper, because you will be able to practice longer if it's at least theoretically possible that you can use the tats you are making. If all the fine crochet threads available are white, you've two choices: buy pastel stationery, or look at the sewing threads. #40 sewing thread is equivalent to #80 crochet thread. All-cotton quilting thread is likely to be strong and smooth; heavy-duty mercerized-cotton sewing thread is also good. Beware of "long staple" sewing threads; these are chopped filaments, and are likely to be fuzzy and weak. Not all "tatting thread" is suitable for tatting; I've bought tatting thread so fuzzy that I had to wax it to be able to draw up my rings.
Choose a fine thread because decorations glued to paper should be thin, and because working fine threads is what tatting is all about. Even if you intend to work on a heroic scale, you have the right to choose to work in mason's line and shock cord, rather than having coarse work forced upon you, so you owe it to yourself to experience the art in its pure form. There will never be a better opportunity to try fine thread than now.
Fine thread will accelerate learning because tatting, like typing, is done primarily by touch. If you can't see your knots, you won't get into the habit of peering at them. If it's impossible to correct your mistakes, you won't waste time picking at them, but will immediately try again.
Most important, fine threads are easier to tat than coarse threads -- they slip through the knots more easily, and they pull up into knots with less effort. Indeed, a fine thread may tie itself into knots spontaneously. If it does, you've lost nothing but a few inches of thread; ignore the tangle. If it gets in your way, cut it off.
When looking at shuttles, you will see huge shuttles for "heavy thread to make the work go faster." If by "fast" you mean that you can produce a twelve-inch doily in a short time, heavy threads do make the work faster. If by "fast" you mean that you can produce knots rapidly and easily, and see how your design works out before you get bored with it, medium and fine threads make the work go faster.
The primary advantage of tatting is that it fits into the smallest pocket. Working in rope and twine throws away this advantage, and does not buy anything to compensate, unless you've promised to make an edging for a bridal bouquet and have to tat nine feet of three-inch lace before the rehearsal.
Let us face it: hand-made lace isn't much use, and even if you work in hair-fine thread, you will end up with shoeboxes of tatting tucked away in your closet. Adopting a less-pleasant working method for the purpose of covering more square feet makes about as much sense as putting a piece of pie through a blender so that you can eat it faster.
Pick the size of thread you enjoy working with most, or a size that will make a shuttleful last a long time, or the size of thread that fits a crochet hook you are carrying for some other purpose, and don't let the zeitgeist stampede you into doing something that you don't enjoy.
Having selected a thread, wind a shuttle about half full and start to learn to make rings. Once again, refer to the pictures in the appendix, or stand behind someone who knows how to tat -- whichever you did when learning the purl and the plain.
Try four or five doubles for your first ring. Fewer won't show as a ring, and more will unduly try your patience. Four doubles are eight half-stitches: four plains and four purls. I find it much easier to count half-stitches than to count double stitches, so I always double the number of doubles, and count that many half-stitches.
In #70 and finer thread, the forming stitches will be entirely between your finger and thumb, so that it is easy to slide them forward on the thread, thereby stretching the ring. You should do so immediately after drawing up each half stitch; if the stitches slip, you have tied the knot correctly. If they don't, you have failed to pull the shuttle thread straight, and the threads are tied together. It may not be too late to flip the knot by pulling a little harder on the shuttle thread. If it is too late, abandon the ring and try again. (Later on, you will loosen a mis-tied knot and correct it, but un-knotting now is a waste of time.)
Since very little thread is consumed by each knot, the ring will grow from this testing. When you make many stitches, it will be necessary, now and again, to slide them backward while pulling the shuttle thread to tighten the ring. This also serves as a test for properly-tied knots.
Some workers slide the thread both forward and back at every stitch, or forward at one stitch and back at the next, and thereby keep the size of the ring constant. Note that such constancy is impossible when working with such coarse thread that the entire ring cannot be pinched at once. It is still possible to pull the shuttle to shorten the ring, but you have to pull on the ring thread with the other hand when you want to lengthen the ring. This is another reason to prefer fine thread for learning.
When the majority of the rings you make draw, start trying the effect of rings of different sizes. You will find that large rings take more force to draw up, and present more opportunities for fatal errors. Any number of stitches, even a single half-stitch, can be drawn up. Three stitches or fewer will make a flat knot which is not obviously a ring; a single plain will make a simple overhand knot in the thread -- but the method of tying enables you to put it at a precise point on the thread; you may find a use for that, if only to make a knotted string to read maps with.
A one-plain ring will form a knot, a one-purl ring straightens out when you try to draw it up, unless you put the shuttle through it first. If you put the shuttle through a one-plain ring before drawing it, it does not form a knot. Try out all four ways of making a half-stitch ring.
You are not supposed to correct your mistakes now, but later on you will need to, so get into the habit of starting to draw a ring, then stopping just before the point of no return. Look at the ring and see whether it is doing what you expect it to. At the moment, this serves only to satisfy your curiosity. Later, the habit will serve as quality control, and also provide a moment to put the shuttle through the ring when you are working on the wrong side. (I'll tell you what "right side" and "wrong side" are later.)
Note that any twist in the ring thread resists pulling into the knots, and becomes concentrated in the part of the ring thread that has not yet been drawn through. Sometimes enough twist accumulates to produce a kink that prevents the ring from drawing. If you pause to put the shuttle-pick or another smooth object into the ring, and stretch the thread to straighten it out, more of the twist will enter the stitches, and developing kinks will be removed. It may be necessary to straighten the thread several times. Some threads kink worse than others, and rings with many stitches present more difficulty than those with few.
If the thread between the shuttle and the ring gets twisted or raveled, let the shuttle dangle and spin.
Leave spaces of unworked thread long enough that you can easily tie the two threads emerging from the base of each ring into a half knot. Tying off is easier to do before you cut the tats apart. It's a general rule that when a pattern is completed, you tie the beginning of the thread to the end in a square knot. For tats, a half knot is enough -- except for butterflies, where you need a visible knot to suggest a head.
When you get bored with making rings of different sizes, make a ring this way: make a double (i.e., work one plain and one purl), leave about half an inch of ring thread bare, and make another double. Note that you will not be able to test for proper tying after making the plain of the second double, because the half-inch of loose thread is not secure until you have tied the purl. After making the second double, push the two doubles together. The loop of thread between them will form a picot. Make two more picots -- each must be followed by a double, because a picot is nothing but a space between doubles. Draw up the ring. You will find four double stitches with three picots sticking out between them. If you were to draw a stem and leaves with green ink on paper, glue this ring to the top of the stem, and trim the protruding threads, it would look something like a little flower. An isolated ring used for decorating paper is called a "tat". You will make many dozens of them.
If the three-picot ring is too complicated, start with a ring of two doubles, one picot, and two more doubles.
Make a few three-picot rings. It is not necessary to push the doubles together, and you may find it easier to make picots of the same length if they are spread out on the ring so that you can see what you are copying. If you make many picots, it will be necessary to push the earlier picots together to make room on the ring, and you can't test your knots or change the size of the ring until you have closed the picots. (To be more precise, changing the size of the ring will close your picots.) It is possible, however, to pull more thread into the ring, then straighten out the last picot so that you can copy it while making the next one. The ring will need stretching more often than it did while you were making picot-less rings, because every picot consumes half an inch of thread.
Once three-picot rings are easy, make a ring with four picots, then five, and six, and so on until you get a ring that looks like a daisy. When you can make picots that are all the same size, try making rings with very short picots, work your way back up to half an inch, then make rings with longer and longer picots until you've made one that is ludicrous.
Try alternating long and short picots.
Make daisies with two doubles between the picots instead of one. If you start and end with one double, the picots will be evenly spaced around the ring, instead of having a gap at the bottom like the flowers made with one double between the picots.
Make a violet: a long picot, three short picots, and another long picot. Tie off and turn the ring so that the long picots are at the top.
Notice that rings with a picot after every double have a definite ring of purls on the "right" side, and a smooth center on the "wrong" side. Sometimes you will use them one way up, and sometimes the other.
Stretching the picots with a pin or pick before tying off will settle the knots -- and you can stretch the under-sized picots a little harder than the over-long ones. Tighten the ring again after stretching the picots.
By this time, you are running out of stationery to decorate. To use tats up faster, draw a graceful curve on your paper with a disappearing-ink pen ("air-erasable" quilting marker). Glue closely-spaced daisies along the curve. You may want to taper the ends by using smaller daisies, or use small daisies and buds to mark out side sprigs. A sinuous curve made of small or medium tats can wind through a spaced row of very large tats. You will think of many other designs made of spots.
If you type your letters, write them first and decorate them afterward.
When you have made enough tats that your rings always draw up and your picots are always the size that you intended, you may move on to making lace -- if you want to. Many people who have gone on revert to making tats, for it's perfect as a nerve-soother: smallest possible equipment, no partly-finished work to haul around, you never have to leave a pattern in the middle (if you get interrupted partway through a ring, you can draw it up and call it a bud), and you can make mindless daisies or concentrate on creating new patterns as the situation requires; you can even change attention levels in the middle of a ring.
The only disadvantage to tat-making is the accumulation of tats. If you are strong-minded, a collection of match boxes and pill bottles will take care of them.
It helps if you know someone who decorates stationery for sale. If you can find a charitable group that decorates stationery or other paper, that's perfect; in addition to disposing of the tats, it takes care of the principle discomfort of doing needlework in public: people who are bound and determined that anyone with thread on his fingers must be making something, and keep picking at you until your answer suits their preconceptions. Saying "It's for the crippled children who make greeting cards at Riley Hospital" will shut them up at once, or at least change the subject.
If you have no way to dispose of your tats, I suggest that you say "I'm making tats, which I offer at a dollar a dozen to people who decorate stationery." Cash in hand is always a credible motive, and someday you may say it to someone who takes you up on the offer.
You can make a picot in the middle of a double as easily as between doubles, but there must be at least two half-stitches between picots, and at least two half-stitches between a picot and the end of a ring or chain. Without the second half-stitch to lock it, a single half-stitch is only a turn round the thread, and it won't stay where you put it. Make a few rings that violate the two-halves rule to be sure that you can recognize the mess when you make it by mistake.
Try making geometric shapes by varying the length of your picots. A star shape is easy, but it is difficult to graduate the lengths of the picots in such a manner that their ends lie on a straight line. Luckily, triangles, squares, etc. look better if their sides are slightly concave. If you make more than four sides, you will have to make the sides concave to make the corners noticeable, and more than five call for a definite star.
Make petal-shaped rings by graduating from short picots at the sides to long picots in the middle. Make three or more petals with no bare thread left between them, then tie the ends of the thread together in a square knot to draw the string of petals into a flower-like circle.
You can make a ring all of one kind of half-stitch to give a buttonholed effect. This is called a "Josephine ring" if you draw it up flat, or a "Josephine knot" if you allow it to indulge its tendency to twist. Small Josephine rings are useful for depicting buds.
Picots can be cut to give a bachelor-button effect. Before cutting, stretch all the picots to tighten the knots at their bases. Instead of tying off the threads left at the base of the ring, trim them to the same length as the picots.
Profile Daisy: instead of picots all around the ring, make a cluster at the tip. Or you can make a "half-ring" -- a ring drawn only until it forms a half circle. A hint of glue can keep the tails under control and prevent the knots from sliding along the naked thread.
Thistle: make a rather long ring with a cluster of three small picots at the tip. Squeeze into an oval before gluing down.
Black-eyed Susan: In yellow or orange thread, make rings that are large enough to have a definite hole in the middle; make the picots close together and fairly long. Make dark-brown or black rings with short picots; these rings should be just large enough to fill the holes of the large rings, with the picots of the small rings overlapping the knots of the large rings. Use the yellow rings smooth-side up and use the brown rings purl-side up.
Butterfly: Make a long picot for the front wing, a slightly-shorter picot for the hind wing, a few doubles for the tail, another hind wing, and another front wing. Draw up the ring and tie the threads together in a square knot to represent a head. You can use three half-knots instead of two to make a bigger head. (This is a short macramé chain.) Squeeze the ring into a narrow oval to represent the body and pull the trailing threads straight out to represent antennae. Dye the antennae black with a felt-tip pen. A very small picot can add definition to the tail. For a challenge, use variegated thread to make the front wings one color and the back wings another color.
Use variegated thread to make a violet with dark-purple upper petals and light-purple lower petals.
Use green thread to make tatted leaves. Twist the two threads at the base of the ring separately, then allow them to untwist together, making a twisted cord to serve as a leaf-stem.