If you hope to build something you can knock down a few targets with in the back yard, or get that opossum to play dead for real, you might be able to put something together. Here are some simple tips.
The key ingredients you will need for a homemade crossbow are going to be a quality stock, jig cut from quality wood. Fashion it to your liking, with or without a grip. Stain it with a good stain and sealer combination product, and allow it to dry for 48 hours.
Next, design a simple trigger mechanism out of steel stock, though at a pinch, a 16 lb nail might serve you admirably. Drill out the stock, bottom to top and run the trigger up through the stock. If possible, use your ingenuity to determine how to lock the trigger once the string has been drawn.
Now, find a durable piece of flexible aluminum. Search your garage or the local home improvement store for stock that will work for the recurve limb. Cut it to length, and sand down the edges to make it smooth. Drill two holes in the center, and secure the limb to the stock with screws at least 3.25 inches long. Coated deck screws will work just as well. Out of heavy gauge steel wire, form a rail, and attach that from underneath, extending out beyond the limb.
Finally, drill holes at the end of each limb, cut your string to length, and tie it onto the limb as tight as possible.
Add any other features to your homemade crossbow to increase accuracy, select some practice arrows and head to the back yard, or somewhere else far enough away where you will not be a menace to anything, or anybody, like the neighbors and their pets. You should probably wear eye protection (and full body armor if you have it!).