Mending damage to drywall is an easy and fairly painless process that can be done by just about anyone with a basic knowledge of common tools. So you've got an ugly hole in your wall that you're tired of looking at and needs to be taken care of. Here's the easy way to do it. We'll just need a few basic tools such as: a hammer, a razor knife, a trowel, drywall nails, sandpaper, a measuring tape, some paint matching the wall in question, a paintbrush, and possibly a sheet or scrap of drywall, and a small amount of the goop called "drywall bedding."
For common minor damage such as a hole in the wall caused by a doorknob, or something smaller, the process is very easy. All you have to do is have your drywall bedding putty (sold cheaply at any hardware store) and a small trowel of some sort. Just use your trowel to put a generous amount of putty in and around the hole, working it in good, then scrape down making the putty as flush with the wall as possible. Allow it to dry for 24 hours, then use the sandpaper to sand it down smoothly, and repaint it and you're done!
For larger holes or damage it's only slightly more involved. First, locate where the damage is and picture a square or rectangle shape that covers the entire area that is damaged. Locate where the nearest wall studs are. (In most homes they are about 1 foot apart horizontally. Now with the razor knife, outline the area around the damage. Keep in mind that you'll need to cut the drywall on the studs about 1/2 inch (most studs will be 1 inch wide) in order to have something to nail your scrap piece of drywall to. After cutting it out you should have a square or rectangle with a 1/2 inch of the closest studs to the perimeter of the damage exposed.
Measure your square or rectangle cut, and then cut a matching piece from your scrap piece with the razor utility knife. (Make sure you have the same thickness of drywall as in your house, the standard is 1/2 inch thick, but it is available in slightly different thicknesses.) After this, make sure the piece fits, it doesn't have to be perfect. It's OK if it's slightly smaller than the hole, but you will have to trim it a bit if it's too large.
Now just take your newly cut piece of drywall and put it in place. Hold it there and nail it in. Be gentle around the edges, drywall crumbles fairly easily. When nailing it in place, try to leave just the slightest indention with your hammer after driving the nail in so that in the next step it can be covered with the putty.
Take the trowel and the putty and fill in along the edges, and over the nails, smoothing it down as much as possible. Then put up your tools because the hard part is done.
After allowing the putty to dry for 24 hours, use the sandpaper to smooth down any rough edges left by the dried putty and repaint to match the rest of the wall.
Hopefully this provides a helpful and inexpensive way to repair minor to moderate drywall damage. Good luck, and happy drywallin'!