There are many ways to repair punctures and dents other bad places in Gypsum Wallboard and type of repair you are trying to make should determine the way you go about making the repair. For dings or dents it is best to just use was is known as drywall compound that is typically used for the finishing of Gypsum Wallboard for this type of repair you use a 5 or 6 inch drywall knife a drywall finishing pan then put a small amount of compound in the drywall finishing pan then you get a small amount of Compound on the knife and pull it across the dent or ding filling it up you then then wipe off the remaining compound back into pan and wipe clean on the edge of the pan now take knife and lay flat on the area at ding or dent and pull the knife back across the area putting just enough pressure on it to get the excess off wipe the knife clean again on the pan now take the knife and wipe the again put more pressure on one side of knife and then do it again but this time put pressure on the opposite side of knife, you let this dry and then do the same thing twice more the same way letting it dry between each time and once the last time has dried you use some fine sandpaper and lightly rub it, you also can use a clean soft piece of fabric and wet it slightly and light rub it down smooth.
When you get in larger repair such as holes in a wall or ceiling anything up to 1 inch or more long and maybe 1/4 to 1/2 inch wide you do this basically the same way except once you put the first compound on it you need a piece of tape over this that is at least 1/2 to 3/4 of a inch longer and wider both ways than the area being repaired, if you are using regular paper drywall tape you cut off with a knife or the drywall knife once you have put it on the area, or you can cut it before put it down also if you do this it much easier to make it blend into the surrounding area and harder to detect a repair has been made, you take the tape you have and tear a tiny little piece off of it all the way around and then put it on the compound in the repair and pull it down as before then once you get it smooth add thin layer of compound over the tape and pull down smooth as before. The torn edge on tape blends much better than the thick square edge the tape. This also requires to more coats of compound drying in between each coat as before and sanding it smooth the same as before.
For larger holes and really bad places that are too big to just use tape and compound to repair you need to cut the hole bigger and try your best square it up, all though it can be longer than it is wide or vice or versa it just easier if you have straight edges to work with. Once the hole squared up as best as can you cut a piece of Gypsum Wallboard to put in the hole you are repairing this has to be at least 2 inches wider than the hole it is going into, in other words you holes 12 inches by 12 inches the piece you cutting has to at least 16 inches by 16 inches or 2 inches wider than hole all the way around, once you have the piece cut turn it over to the back mark it with a pencil in 2 inches from the edge all the way around, then take knife and cut it on the pencil mark all the way around only on the back once you have done this you push it down and push it on the edge you cut it will peal off and leave the face paper of the board there undamaged do this all the way around check closely to be sure there isn’t anything left on the back of the face paper, this should leave it to be a tight fit the hole in the wall or ceiling if it is to large to fit trim it a little at the time till it fits once it does fit it in the hole and fold back the paper on the edges and then spread compound all the way around the hole at least 6 or more inches out from edge of the hole and up against the edge of the hole and then push the fold back edge down into the compound all the way around and pull it down as tight as can like you would a tape joint once you have it smooth add more compound and smooth that out as much as you can and let it dry this also requires at least two coats of compound and then sanding it smooth. If the areas is larger than the 12 inch by 12 inch or you feel like you need some extra support behind it you use a piece of plywood, wood stud, Metal stud or even a strip of Gypsum Wallboard about 4 to 6 or 8 inches longer than the width of the hole, cut it and place in the hole in the center and up against the back of the hole and place 2 screws thru the Gypsum Wallboard and into the piece in behind on each side. You can take Compound and spread it on the piece you just placed and screwed into place. Then place the piece you have in the hole according to above instructions and add compound and smooth out and then add compound and smooth twice more after drying and sand smooth.