You can buy your own catapult at your local Walmart for around $10.00 USD but it is more fun to build it yourself. I built mine for free since all the components I used are from recycling materials...
Step 1: What you will need
For the slingshot, try to get a V shape branch from a tree like depicted on the picture. You'll also need to large and robust rubber bands and four smaller ones. Finally I use a 1ft vinyl baseboard piece for the sling but you can use what you have such as an old leather strip from a shoe, belt etc.
Step 2: Sling preparation
Cut the two large rubber bands and cut the vinyl base into the shape depicted on the picture.
Step 3: Sling assembly
Take one large rubber band and bind it very tightly to one side of the vinyl sling using one smaller rubber band. Repeat the operation for the other side.
Step 4: Attach the sling to the slingshot
Once the sling is together, attached it using the same technique as the previous step to the slingshot using the two remaining rubber bands. And you're done !