Step 1: Gather the Materials.
Craft foam - I use 1/16" thick.
Masonite - Backing of old picture frames can be a good source.
A handle - Ordinary knobs from a cabinet door works well.
Countersunk screw for the knob (optional).
Pocket laser engraver (Optional) ;)
Step 2: Creating the Cutout.
If you use something like my small laser cutter all you need are to load up some craft foam and press print. Otherwise you can print the shape onto thin paper. The thinner you can find the easier it is to get a good result. Now glue it to your craft foam using a glue stick by putting some glue on the paper and press it down onto the craft foam. With a sharp knife and scissors follow the lines to make your pattern. If you want to make small holes or other pattern that is hard to do with a knife you can heat up a straightened out paper clip over a small candle and gently press it down into the foam. That is how I did the fins on the arrow of this design, only I used a small screwdriver as I didn't find any paper clips. When working with heat like this it is easier to work from the bottom of the foam, this is the side you will have the ink on.
When you are happy with your cutout it is easy to remove the paper. Just drop the whole thing in a glass of water and the glue will dissolve and fall off.
Step 3: Putting It All Together.
Drill a hole in the center of the Masonite and countersink it carefully. With a countersink screw you can screw on the handle and still have a flat surface for your design. Another method is to skip the screw and just glue the handle onto the Masonite. This is a lot easier but with the risk that the handle breaks of if someone is a bit rough. I glued it as I could not find a counter sunk screw.
Lay out your craft foam design the way you want the stamp to look. Now just put a little glue onto the craft foam and press down the Masonite carefully onto the pattern. Be sure to align the pattern in the center of your handle.
Thats all there is to it.