What tools are needed to fix a hole in drywall?

If it's a small hole, like from a door knob, all you'll need is a big putty knife (called a taping knife) some wall board compound and some of the mesh type drywall joint tape.
Put a thin layer of compound on the wall, mush a couple of strips of joint tape into it and smooth it with the taping knife.
Leave it dry overnight. The compound shrinks as it dries and you'll probably have to add 1 or 2 more coats.
Thin coats dry faster and smooth easier. Sanding the compound makes a pretty big mess so go easy, if you're careful all you'll have to do is touch sand it at the end.

If it's a big hole, like somebody got their head slammed into it, you'll need to cut out the damaged area with a drywall saw (sometimes called a keyhole saw).
Get a couple of pieces of scrap wood, stick them in the hole so they bridge across it and run some drywall screws thru the drywall and into the wood to keep it in place. Don't drive the screws in too deep, you can actually drive them right thru the wallboard. Tighten them only enough to fill with a thin coat of wallboard compound.
Cut a piece of wallboard to fit into the hole. (It doesn't have to be a tight fit) Screw thru the patch into the wood you added. Don't push too hard on the screws or you'll tear the wood loose from the wall.
Use the same process on the joints around the patch as you would to fill a small hole.