You will need two squares of fabric measuring 4" by 4". Of course you can change the dimensions if you want, but this is the size I like.
You will also need 16 gauge clear vinyl. The thickness is very important because thinner vinyl might warp when you put a hot mug on it. I have found the 16 gauge works great. I like to cut the vinyl a little larger than the fabric squares so I don't have to worry about the edges staying perfectly lined up - you will trim them later.