Here are some cookie puzzles I made for pre-school today.
I used a sugar cookie recipe that I've always loved.
I cut the dough into squares and placed two squares on a cookie sheet. I then cut out what I wanted and baked according to the recipe. When they came out, the shapes were still easy to discern. I waited until they cooled off and then went around the shapes with a knife to make sure the "puzzle pieces" could come out. I took the puzzle pieces out and frosted everything separately with colored powdered sugar frosting (Powd. Sug., vanilla, and milk) and let the frosting harden. Once everything was dry and done, I placed each cookie puzzle on a nice napkin and put them together for the kids for the next day.
I didn't worry about making some kind of a "grip" for each piece. I saw on the recipe that I was looking at that someone had baked almonds into the cookies so that the pieces could be pulled out.