First, here's my die cut and my foam. (The sheet was 49 cents, but you can get it cheaper, I just wanted to buy one to try the project first).
Now, you can do this next part in two ways. If you are only using the stamp for a current project and don't intend to save it, you can attach it to a clear acrylic stamp block. Use some scrapbook adhesive, but before you just stick it on the block, rub it on your shirt/sweater a couple of times. This will make the adhesive tacky, but less likely to permanently stick. All you really want is for the stamp to cling to the acrylic block.
Then just ink it up like you would with any other stamp:
The other way to do it is if you want to save the stamp for future use. Attach it permanently to a block of wood, like a rubber stamp. If you've got a handy woodworker husband, like me, you can have him cut you up some scrap wood into stamp sized blocks:
I thought I might use this stamp again, because it came out really nice! Now I've got my own custom stamp, all from a die cut and fun foam!