A friend of mine showed me her potholders like this, a few years ago. I've been intent on trying to make them ever since. I finally found out how to make them with enough searching. Bev, over at Bev's Country Cottage shows how to make these simple yet effective potholders.
It's actually quite simple to make as it only requires single crochet throughout the project. The type of yarn to use is debatable. Some say that wool or cotton is the only way to go, while others say that acrylic is perfectly fine. From the online debates I'm hearing, I'm going to make the conclusion that wool or cotton is the safest bet, especially if you're going to give these as gifts. However, acrylic will work perfectly fine if you intend to use for temperatures that aren't too high (less than 400 deg, for instance). Anything higher than that, will melt the acrylic and potentially cause burns. To be on the safe side, use cotton or wool. By the way, this is a perfect way to use up remnants of cotton yarn.
Okay, so here's how I did it.
Start next row by single crochets on the bottom side of the ch by turning the piece clockwise and continuing to sc til the first ch.
Turn the piece clockwise again and crochet another row of single crochets onto the other side of the first row.
Continue to do single crochets around and around (do not increase stitches).
As your potholder grows, you'll notice that the first row of 35 chains is actually a diagonal of the backside of the potholder. The potholder will grow and basically turn onto itself until the two sides of the potholder will meet together to form the front side diagonal of the potholder, and can be crocheted closed together with another row of single crochets. I just hold the two edges together and and single crochet thru both edges (together) to close and finish the potholder.
These thick potholders work great, are quite convenient, and can be thrown in the wash when it gets too icky. :) Plus their quick and easy to crochet. Once you're done, you can hide any excess string inside the potholder.