I found this tutorial on a blog I love and went through my fabric stash and happened to have enough of everything to make the mat. The big pieces came from remnants I bought a year or two ago with nothing particular in mind (see honey, I finally used them) and the smaller pieces were from a dress I made Baby Girl a couple of years ago.
I followed instructions on the tutorial almost exactly, with the exception that I stitched small pieces to the top to make the pillow since my big pieces of fabric weren't long enough, used Velcro instead of buttons on the tabs to make it easier for my toddler to handle by herself, and used cotton quilt batting instead of 1" foam (because I don't happen to have big pieces of foam laying around). The batting was twin-sized and I just folded it all up evenly to insert into the mat.
The beauty of this style nap mat is that A) it's easy to make, B) has a great strap for transporting and C) is easily washable by removing the batting or foam insert.