First, make a pattern. Your yo-yo pattern needs to be twice as wide as your intended yo-yo, plus about 1/2" for seam allowances. You can use a compass to draw out your pattern, or find a bowl or lid to trace. Chipboard works great for a pattern, as does the cardboard from a cereal box.
On the wrong side of your fabric, trace around the pattern. Use a water-soluble pen or chalk. Following your traced line, cut out a circle of fabric.
Fold under a scant 1/4" along the edge of your circle, as you stitch close to the folded edge. Use strong thread and make sure it's long enough to go around the full circumference of the circle, with some to spare.