You can use a drywall patch up to about 8 inches of a hole. Anything larger than this usually requires some pieces of drywall for the rigidity to span the space.
Repairing small holes in drywall can be done with a simple patch. These drywall patches can be purchased at most local hardware stores like Lowe's or Home Depot. The patches can be applied directly over the drywall holes. You just need to make sure the hole is clean and smooth so the patch can stick properly.
After the patch, you will apply drywall joint compound or spackle over top of the patch and smooth it out. This drywall repair usually fixes holes and drywall cracks.
If the drywall is cracked or chipped, you can use drywall compound to fill it in first. This will help smooth out the drywall further so that there are no ridges or bumps after applying the drywall patch.
If the hole is larger than 8 inches, you should follow these steps: