Step 1: What You Need
Bottle caps (24 - 12 of two different designs or colors).
Clay (I made my own using a simple recipe I found here: http://chemistry.about.com/od/chemistryactivities/a/modeling_clay_recipes.htm (I used the first one)).
A butter knife to cut the clay
Something for the base (I used vinyl because I had some laying around. Felt or some other fabric would probably work well, if not better. Or I suspect a nice coating of glue would do the trick).
Scissors (To cut out your base fabric, and to trim it when it's dry).
Step 2: Using the Clay
Squish the clay in to make sure you don't leave any gaps. Use extra bits of clay if your cut was too small, or remove excess if it was too much , and smooth everything out.
Step 3: Allow to Dry
Step 4: Adding Bases
Put a nice layer of glue on the bottom of each checker, and add the bases. Allow them to dry well.