One of the most important facts that you need to realise before mounting a pegboard on drywall is that a small amount of space must be left behind between the drywall and the pegboard. This is important because the hooks and pegs used on pegboard are designed so that they can be inserted through the pegboard holes and the hooked from behind the board.
In order to provide space between the drywall and the pegboard, you will need to install a wooden frame on the drywall first. Use a stud finder to locate studs behind the drywall and mark their location. Once you have located an appropriate number of wall studs, scribe a horizontal line which passes through the stud marks. This line will serve as a reference for you to install the wooden frame.
Using the scribed horizontal line as a reference, install a horizontal wooden strip and driver screws which go all the way to the studs for adequate support. Make a wooden frame work by finding more studs behind the drywall and then installing more wooden strips. You may want to install a few vertical strips of wood for median support.
Use a jigsaw, circular saw or table saw to cut the pegboard in desired shape and size. Make sure that you do not cut the pegboard using a utility knife or any other hand tool because you will never end up with a clean cut if you do so.
Place the pegboard against the wooden frame that you created earlier and hold it in place with one hand. If the pegboard is too large, you may want to ask a friend to keep the pegboard pressed against the wooden frame. Install wood screws along the length of the wooden strips at the back of the pegboard. Use a cordless drill with screwdriver attachment for this purpose.
You have successfully mounted the pegboard on drywall. You can now go ahead and arrange as many hooks as you like on the pegboard so that you can put the pegboard to use by hanging tools on it.