Miss Piggy's blonde wig, which has holes for ears and therefore stays in place very securely, gave me the idea of trying to make her a wig myself. This is just the first version and I'm sure I can improve it.
The basic structure is very simple, just a piece of fabric attached to a rubber band.
Measure the rubber band so that it goes around the ears snugly, sew it into a loop and sew the fabric strip to it. The fabric in this one was first sewn into a tube to prevent fraying and to make it a bit sturdier. If you use thick fabric, just one layer is probably better.
Finally, sew yarn into the fabric as shown in these pictures of the finished wig. You'll need quite a lot of it to get a wig that covers the entire head.