You need the completed embroidery, a cardboard circle, a needle and thimble, an iron, a firm ironing surface, a safe place to set down a hot iron, a press cloth (any clean rag), and small pointy scissors.
(If you are an adult or have a parent's permission, there should be a razor blade in a cardboard sewing kit in your bag. If you are careful, a razor blade will substitute for small pointy scissors.)
Thread your needle with strong thread. There should be a piece of strong thread in the cardboard sewing kit in your bag.
There should be a dashed circle around your embroidery. Running-stitch around the circle with strong thread. Try to take two stitches per dash. End with both ends of the thread on the right side of the fabric.
Tie the first half of a surgeon's knot in the two ends of the strong thread. (A surgeon's knot is just like a square knot, except that you wrap the thread twice instead of once when tying the first half, which makes it easier to pull it tight.)
Draw up the stitches until the fabric is gathered all the way around the circle, then stretch it enough that you can put the cardboard circle inside.
Pull the ends of the thread until the fabric is tight around the cardboard circle. If necessary, push and pull until the cardboard is centered inside the embroidery. Finish tying the surgeon's knot. Don't trim the ends at this point.
Put the medallion right-side-down on the ironing surface and press the edges with the tip of the iron all around. Pull firmly on the excess fabric while ironing, in order to make the gathers orderly. Ease out the gathers as much as you can.
Trim off excess fabric with small pointy scissors, pulling on the excess fabric all the while so that you can see what you are doing. Leave at least a quarter inch of seam allowance.
Cover the medallion with a press cloth and press firmly with the hot iron, then twist the iron back and forth to get the trimmed edges nice and flat.
Trim the ends of the strong thread to between a quarter inch and half an inch long (6-10 millimeters).
If you wish to cover the back, you will also need a paper circle, a glue stick or some paste, two pieces of waste paper (each with one clean side), and something smooth to rub it down with. I usually use the closed glue stick, which has a smooth cap. The back of a teaspoon will work.
If you want to write on the paper circle, do so before putting glue on it.
Put the paper circle face down on the clean side of waste paper. Stroke the glue stick from the center over the edge, so that every little point gets glue on the back. Lift it off, careful not to get glue on the front. (Crumple or discard the dirty waste paper at once, so that it won't be mistaken for a clean piece.)
Put the medallion face down on a hard surface and lay the circle glue side down on the back. Press in a few places to stick it enough to keep it from shifting. Lay the other piece of waste paper over it with the clean side down. Rub firmly through the paper, paying special attention to the edges of the paper. The waste paper will probably become embossed with the shape of the medallion underneath it.
Also crumple and discard this waste paper at once, as it may have glue on it.
To attach a ribbon with a steel crochet hook, work the hook through the fabric, just missing the cardboard, then push a little farther to make the hole a little bigger. Catch the middle of the ribbon and pull a loop through. Pass both ends of the ribbon through the loop and pull them snug.
If you have no crochet hook, fold the ribbon in half and put the loop through the eye of your needle. Push the needle through the fabric, trying not to pierce the threads. If the fabric is loosely woven, you can put the needle between the threads eye first. Pull the loop through, pull the needle off it, put both ends of the ribbon through the loop, snug down.
It the eye of the needle is too small to thread ribbon, use it to push a loop of strong thread through, put the ribbon through the loop of strong thread, use the loop of thread to pull the ribbon through the fabric.