This is an easy way to make rubber stamps that you design and that will last for many stampings. The first one I made has lasted for over 500 uses (up to 75 uses in a single day) and is still as clear as the day I made it.
Step 1: Materials
You will need: thick craft foam and thin craft foam, scissors and/or hobby knife, cutting surface, wooden spools and flat shapes, glue, toothpicks, cotton swabs, and a clamp.
Step 2: Base pieces
Choose a flat wooden shape and a spool, and cut a piece of the thick craft foam slightly smaller than the wooden shape.
Step 3: Gluing the base
I used gorilla glue, which expands into the parts it glues, so I think it might expand into the tiny holes in the foam as well as into the wood grain. I think you could use the "foam glue" or even regular white PVA glue like Elmer's.
Gorilla glue is a polyurethane and is activated by water, so you have to get a piece of what you are gluing damp. I dampened my wood square on both sides and applied a thin layer of glue to the thick foam and to the spool using a toothpick.
Step 4: Clamping the base
Let the glue set for an hour in a clamp. I used an extra wood square to prevent the clamp from creating a permanent dent in the middle of the thick foam, since that is going to be the backing for the actual stamp. While waiting for the glue to set, design and cut out your stamp.
Step 5: Cut the design
I tried several designs before deciding on which one to use. Cut the design out of the thin foam using scissors or a hobby knife. Try to use up as much of the full stamp shape as possible.
Step 6: Check the design
Remember that when you attach the design to the base, you will have to put it on "backwards" in order to get a "frontwards" image when using the stamp. Double-check to make sure the design will fit on your base, and make any necessary adjustments with the knife or scissors.