Fold under 1/4-inch of fabric. Thread a needle with sturdy 100-percent-cotton thread and knot the end. Take small, evenly spaced running stitches near the folded edge all the way around the circle. Bigger stitches will allow the fabric to gather more.
End your stitching just next to the starting point; don't knot or cut the thread. Gently pull the thread end to gather the folded edge until it forms a gathered circle. The right side of the fabric will develop soft pleats as you gather the edge. Take a small stitch to hold the gathers in place, then knot your thread and cut off the end. Backstitch over the knot so it doesn't pull out.
To join yo-yos, place them with the gathered sides together. Using matching thread and small stitches, whipstitch them together for about 1/2-inch. Make rows of joined yo-yos, then sew together the rows in the same way.