I found some gently used burp cloths that I wouldn't mind giving up. You really need to use this shape of a burp cloth since it creates the purses shape.
Then, I folded the burp cloth in half. Once it was folded in half I pulled down one side until I had it a the length I wanted it to be. This flap will become one side of the purse.
Then, I pinned the flap down and sewed it in place. This is what you want it to look like (see above). Then I took some extra fabric I had on hand and created a little strap for the purse. You could also use ribbon. Once I had my strap put together I folded the burp cloth in half again and pinned my edges together. Make sure you insert your strap into the edges prior to sewing you sides together (as seen below).
Once your edges are sewed down you should have a little pocket and flap that closes over the top of that...like so.
Then, I used some velcro to create a little "snap" to shut the purse together. And finally, I added a little button to the exterior flap to give the look of an actual snap.