Loosen the guitar string so that it does not snap or injure you when you replace the peg. Do this by turning the tuning peg to loosen the string or remove it entirely.
Unscrew the peg until it comes off of the guitar.
Screw the new peg into the hole. Make sure that when you purchase the new peg, that it is either the same size as the old peg or a bit bigger.
Place a small amount of wood putty into the hole if the peg is too small or use the reamer to make the hole a bit bigger if your new peg is far too large for the hole.
Replace the string around the tuning peg if you removed it in Step 1.