I can't remember where I learned how to make this apron. I know I've been making these for about 5 years. Fold the dishtowel in half from side to side, cut the top corners off with a rounded edge, and use bias tape to make the waist ties, enclose the raw edges, and make a neck tie in one fell swoop.
I used to keep the bias tape in one long piece and guess at how big the neck hole needed to be (to fit over a head and yet not hang too low in front). In the past I've also used two D rings stitched to one corner so the neck strap could be adjusted. Now I've decided it's just as easy to make a loop from the bias and the wearer can just tie the neck strap where they want it:
If you're lucky, you can find a thrift store that has a sewing section and get your bias tape for a huge discount. Otherwise, I suggest you make it yourself. That link has photos, this link has line drawings.