Well here's a website for a catapult, all you need is - newspaper, tablespoon, rubber band and masking tape. http://funadvice.com/r/15i6jfvm41j For this one you need: Styrofoam, a plastic spoon, 2 plastic forks and a rubber band. -stick the forks in the Styrofoam (the part you eat with goes into the Styrofoam), stretch the rubber band around the forks and then put the spoon in the gap the rubber band has. the part you eat with up.
If you want a more advanced catapult then there's this one: http://funadvice.com/r/15i6jfvm5bc You need: a hammer, saw, screwdriver, pliers (needlenose), wood Glue, file, scissors, drill and bits, sandpaper and cutters for metal. Good luck!
To make a full size catapult you will need a lot of wood, rope, and something large and heavy for a counter weight. But the basket that holds the ammunition you will be firing can be made of a pillowcase or blankets. Good luck! I want a catapult!