You won’t need ground-breaking tools or materials:
Firstly, peel and scrape all the bark from your fork. This will allow the wood to dry efficiently, and gets rid of any discomfort the bark might have caused. To dry it you can either chuck it in a cool, dry place or put it directly in the sun. The “cool, dry place” is the best way because the wood dries out evenly and has less chance of splitting. Wood that is dried in the sun or using an oven or kiln dries out faster and may crack, weakening the wood.
It’s smart to trim and cut your fork while it’s still green to remove any knots or funny bits. The optimum length of the arms is the length of the handle, so make all the pokey-out bits an equal length.
Once the wood is dry you can Cordwrap the handle if you want. Cordwrapping makes the slingshot comfier to hold and draw (use the highest ply of yarn you can find for a really soft grip), as well as making it look spiffier.
Read on for instructions on making the firing assembly.