That ugly hole in the wall from a door knob can be a pretty simple fix.
Find yourself a piece of scrap 1/2 inch drywall about three times the size of the hole.
Score the backside of the drywall allowing about 1" to 1.5" on the edges.
Snap the edges off of the repair piece and leave the paper on the front. Make sure to clean off any remaining drywall from the paper.
Line up the repair piece to cover the hole and any damage portion of the wall.
Trace around the edge of the repair piece to mark the cut line.
Cut along the line with a box knife or drywall hole saw.
Dry fit the repair piece to make sure it fits flush. Be sure to mark the direction that the piece fits.
With a 6" drywall knife, spread drywall mud around the edge of the hole and on the inside edge of the repair area. It's a good idea to add a little mud to the edge of the repair piece as well.
Insert the repair piece into the hole you prepared in the wall. Use a 12" drywall knife to push the piece in flush working the excess mud out from under the edges of the paper.
Before adding your second coat of drywall mud. Make sure that the first one has dried. Resist the urge to finish this with one coat. The mud shrinks as it dries so plan on 3 thin coats to finish.
After your last coat has dried, use a damp towel to sand the surface and blend the edges. You are now ready for primer and paint.