The diameter of hole size that needs to be repaired has everything to do with the way it is patched, and finished. There are many proposed methods of treating these repairs in the wallboard. But by sticking to proven methods you are far ahead.
The hole that is narrow, say the roundess of a pencil or less, is the easiest to fix.
1) First, view the surface of the hole up close. After removing the object that has caused the hole, usually the wall portion of a screw anchor, see if there is a much of rise around the small opening. Commonly when enough force has been exerted to push through the wallboard, a small outburst is left since many anchor styles act to compress the gypsum when inserted. Depending on the degree of rise, tap with a nailset and hammer to countersink. Tap with only enough force to set level with patch, and no more.
2) For the tiniest of holes, like a small nail. press a small dab of compound into the opening with a slim putty knife, filling to some depth. Then give a wipe clean in circular motions around the border to blend off. Done with some finesse, you are then done with no sanding. But wait until dry to be sure.
3) For holes, say the diameter of a pencil, countersink as you would usually but apply compound in two steps. Filling the void in the first, which will settle some, then sand off lightly. And apply the second coat and sand when ready.
Moving out of the smallest hole sizes and into wider openings, the repair takes a technique that will provide some structure to the fix.
Patches up to 3 Inches Across
The increase in hole sizes normally require added reinforcement for the patching compound. To repair penetrations through the drywall up to 2.5″ to 3″ structural technique is applied. One that takes advantage of the virtues of mesh tape.
1) Clear the inner edges of the hole. Remove any loose chunks and semi-attached pieces of gypsum which happen to be there and cut free any compromised paper membrane on the surface. Using a sharp breakaway knife will leave a clean edge but be sure to wear eye protection.
2) Determine the hole size and firmly press on mesh tape to cover the opening, intersection the tape at 180 degrees, forming a cross. For holes in the smaller ranges, apply 2″ wide tape, and for holes spanning to 3″ apply 4″ wide fiberglass mesh. Make certain there is enough surface area on the tape for sticking on the wallboard. Adhering with greater than 1/2″ at bare minimum anywhere.
This will give a double layer of tape coverage over the hole entrance, and the adhesive backing needs no embedding. Make sure to make clean cuts in the tape – the fiberglass will naturally want to fray and the mesh should be without any lifting strands whatsoever.
3) With either multipurpose compound or a quick dry mix, from powder form, knife on the mud with a 4″ knife blade. The mudd should be thin enough to flow down through the mesh backside and yet hold form without sagging. Press the blade evenly and flatly across the tape. Cover to a thin layer extending over the tape edges to a gradual float, depending on hole size.
4) After thoroughly dry, superficially abrade the surface with a sanding block or sponge. Have a sheet of plastic below to keep the dust off the flooring.
A fine grit sander is best, particularly if surface is to receive paint having any gloss. Scratches from rough papers will show through.
5) Apply another coat of compound, broader still, and sand to finish after drying. Expect dust with an increase in patch sizes. If an even level has not been gotten, repeat until it does.
Other Patching and Repair