The most common way to tat is to work back and forth over one section of the ring. I prefer a rotary motion, making the same pass over the front and the back of the ring. The rotary motion is quicker and smoother than the oscillating motion. It does have two disadvantages, but the second is no disadvantage at all, and I'm not sure about the first.
The first disadvantage is that because the motions for plain and purl are the same, you tend to count half stitches instead of doubles. If you want four ds per section, for example, you will work to a count of eight. As compensation, the only difference between working on the right side and working on the wrong side is that plains are odd numbers when you work on the right, and purls are odd numbers when you work on the wrong. It might be that the prevalence of the oscillating method of tatting is the reason that the distinction between right and wrong is so often neglected.
The second disadvantage is that the rotary method cannot be used when you are working with a sewing bird. The thread has to slip over your middle finger each time you work a purl by the rotary method, which is impossible when a fixed clamp replaces your middle finger. The solution, of course, is to revert to oscillating tatting when working with rope and twine. The motions have to be modified so much when tatting twine that you'll probably find the purl easier than the plain, because you won't have as many false expectations about it.
>>..++the diagrams mentioned below have never been drawn
There is intellectual discomfort in rotary tatting: how can doing exactly the same thing produce mirror-image effects just because you do it in different places? To explain, I present a series of diagrams of an invisible embroiderer doing up-and-down buttonhole, which is tatting without the complication of flipping knots from thread to thread.
The first three drawings explain how up-and-down buttonhole is worked in real life, which is why the glossary entry for "up-and-down buttonhole" referred you here. Notice that our worker first makes an ordinary buttonhole stitch by pushing the needle up through the cloth, then to produce a mirror image of that stitch, he first pushes the needle down through the cloth, then tightens the thread by pulling it up.
In order to see what is going in in the second half of the stitch, drawings Four and Five leave out all but one thread of the cloth, and add a mirror image of our invisible embroiderer on the other side of the fabric. After making a buttonhole stitch with his right hand, he hands the needle to his twin on the other side of the fabric, and the twin makes a buttonhole stitch with his left hand. If you imagine the needle in figure five rotating toward you, you will see how the gyrations of figures two and three produce the same effect as Figure Five without the need to walk around the fabric and work from the back.
The embroiderers first work a loose loop, and then pull it into a knot. Suppose the left-handed twin were to work his loop very loosely. Then you have Figure Six. Bend figure six toward you to make Figure Seven. Now our left-handed twin is standing with his back toward you, like his right-handed brother.
If up-and-down buttonhole is as easy as this, why do we want to introduce the complication of flipping the knot from one thread to the other? Because up-and-down buttonhole is about as fast, easy, and graceful as it's ever going to get the first time you work it. Tatting seems awkward at first, but with a little practice, you can form the knots as fast as you can flip the shuttle. Moreover, by flipping the knot, you are able to form it by feeling the tension on the threads instead of by watching the knot. Working by touch was important to our ancestors, who used invisibly-fine thread, and still important to people who carry coarse thread in their pockets, to work amid distractions by whatever light is available.
Now you are prepared to see what is happening when you tie plains and purls with a shuttle.
Get ready to chain by looping the thread around the little finger on your left hand. Hold the end of the ball thread in your right hand, dangling down in front of your left hand as in Figure Eight. Sweep your left hand toward you, up, and back, catching a loop of the thread as in Figure Nine.
Bring the end of the thread around the backs of the ring and middle fingers to be grasped between the index finger and the thumb, as in Figure Ten. The middle finger holds the loop open, and the ring finger presses down on the thread to keep the loop around the little finger from slipping. The thread will slip quite frequently while you are getting the hang of it. When it happens, pull down on the thread dangling below the little finger in order to tighten the loop again. When things go completely haywire, transfer your work to your right hand and pick the thread up the way you did in the beginning.
When the loop becomes too tight, allow it to slip on purpose -- enough, but not too much. Controlled slipping also takes practice, but eventually you'll find that there is always the right amount of thread in the loop without your conscious intervention.
Now add the shuttle thread; grasp it between the thumb and index finger alongside the ball thread (Figure 11). At this stage you won't be using enough shuttle thread to need to wind it on a shuttle, but I've drawn a pointy oval on the end of the shuttle thread to identify it. In each drawing, I've drawn only enough of the thread to show where it is going, so it will appear to vary in length.
Begin the cycle at the point where the shuttle is beyond your left hand, so that the shuttle thread dangles down on the far side. Bring the shuttle back toward you, across the thread between your index and middle fingers, then push it forward under the thread (Figure 12).
Now pull the shuttle up, making sure that it passes under the ball thread and over the shuttle thread (Figure 13.) Pull the shuttle thread tight while slightly relaxing the ball thread, causing the knot to flip into the ball thread (Figure 14). Keeping the shuttle thread tight, tighten the ball thread, causing the knot to run up against the thumb and index fingers (Figure 15). Pinch the new knot between finger and thumb, pushing it slightly forward on the still-taut shuttle thread. This completes a plain.
Now that the plain is secure, bring the shuttle toward you, allowing the shuttle thread to dangle on this side of the loop. Push the shuttle up under the thread between the little and middle finger in the same way that you pushed it up under the other side of the loop when making the plain. This time the shuttle thread is to the left of the shuttle, so the shuttle passes neither under nor over the shuttle thread (Figure 14). As you tighten the shuttle thread, nod the middle finger slightly to let the knot pass over it (Figure 15). This may give you grief at first, but keep calm and persevere; eventually the nodding of the middle finger will be exactly the same as the loosening of the loop that you did for the plain, and you won't be aware of passing any obstruction. Once again, straighten the shuttle thread and run the new knot up against the first one (Figure 16). This completes the purl, and leaves the shuttle at the far side of the left hand, ready to begin a plain.
Now you need enough shuttle thread that you will have to wind it on a shuttle.
When you make a ring, one thread serves as both shuttle thread and ball thread. Begin by pinching the end of the shuttle thread between index finger and thumb, then bring the thread down behind the fingers. This puts you in the same position you would be in if you had picked the shuttle thread up for a ball thread, then let it slip off your little finger (Figure 17). This part of the thread will be used like the ball thread, and when you need more, you will pull it off the shuttle in much the way that you pulled more thread off the ball. Since there is no longer any ball, I will call this part of the thread the "ring thread."
Bring the shuttle thread up in front of your left hand to lie beside the end of the ring thread between your thumb and finger. Your ring finger has nothing to do, now, but otherwise you form the stitches exactly as you did when making chain. (Figures 17 and 18.) The stitches can be slid back and forth on the shuttle thread to adjust the size of the ring. When the shuttle thread threatens to become too short for comfort, unwind more. When you alternate between rings and chains, it will be necessary to wind up the thread before each chain and unwind it before each ring, because you need more shuttle thread to make rings.