Drywall – New House, Horribly Patched Drywall

Patching:

When patching smaller holes, a 6" taping knife should suffice.

Apply the compound in a few light coats rather than a single heavy coat, and sand between each coat.

You can either sand the patch using a sanding block like the 3M® Fine/Medium Large Drywall Sanding Sponge,

or wet sand using a slightly damp rag. If you choose to wet sand, let the area dry before applying the next coat.

For larger holes, you'll have to fill the hole with something solid before you apply compound (don't try to fill the hole with mud). Once the hole is filled, start with a 6" taping knife for the first coat. Next, apply a few thin coats using a 10" taping knife

feathering the compound out to blend into the wall.

When working with drywall compound it's a good idea to use a Hawk, or a mud pan instead of working directly from the bucket. This will insure that you don't end up with little bits of junk in the compound, and that the compound in the bucket won't dry out too much while you're working. They are also good for catching falling mud.

Preparing the wall:

Wipe the wall down with a dry rag, to remove any dust and dirt. Prime the whole wall with a proper primer, like Glidden Gripper.

Any time you patch, it's a good idea to prime the entire wall. If you simply prime the patches, you may be able to see the patches when you're done.

Painting:

Apply 2 coats of the desired paint, and you're done.

If the patches were done properly (smooth and blended appropriately), after primer and two coats of paint you'll never know there was a patch there.

NOTE: Products mentioned in this answer are for example only, I do not specifically endorse or recommend the use of any products mentioned.

It's a patch - you don't need a special screwgun, you don't need ANY screwgun.

Use screws - nailing drywall is an art form and takes a special hammer. Screwing is easy and takes a Phillips screwdriver. If you use a "not special drywall screwgun" stop before the screws are all the way in and use a screwdriver to finish. The head of the screw should end up just below the surface, but not so far that the paper breaks. Practice a couple on scrap - start with going too far and then you know what not to do - get a couple just right before you start on non-scrap. Backing up after you go too far does not work - the strength is gone when the paper breaks. If your shortest knife run across the surface does not hit the screwhead, it's deep enough.

You don't really need 3 knives/trowels (knife, ala puttyknife, is more common in this context) for a patch, either, though they are nice to have when doing a whole room (same applies to the screwguns, which can be rented when you have a whole room to do.) A big one (12") and a small one (3-4") should be sufficient, but if you want to be over-equipped for this job or equipped for the next one, add an 8". Try a yardsale if you can find one, if cost is an object.

Mud lingo - don't get too concerned, it's a patch, you want standard mud that you can get in a small (4 lb or so) tub. There's rarely a choice in that size. Since you don't say what mud lingo you don't get, I'll go into a few - hot mud is dry powder you mix with water that sets quickly (the number of minutes it's supposed to be workable are usually in the name.) Standard mud comes as a paste in a tub or bucket, and dries rather than sets. Lightweight mud is like standard mud, but lighter (almost foamy.) All "mud" is actually labelled as "joint compound" but pretty much universally referred to as "mud"

The secret to mudding is to get it on good enough and stop, let it dry, and then put on the next coat. Trying to make the first coat "perfect" usually makes it worse than if you stopped 20 minutes earlier. It will shrink when it dries anyway - the multiple coats of mud serve to fill smaller and smaller defects, so there's less fresh mud, so it shrinks less each time.