Insert the hooked tip of a nail ripper underneath the broken slate and hook the ripper against the nail located at the top of the slate.
Cut through the slate nail with the nail ripper to free the slate. Note that the top of the nail ripper's handle features a metal plate. Strike that plate with a hammer to cut through the nail.
Slide the broken slate away from the roof.
Scribe a cut line across the new slate piece with chalk. The new slate piece should be the same length as the surrounding slate pieces on the roof.
Punch a series of holes along the length of the cut line using a nail set and a hammer.
Position the slate piece between two pieces of wood so that the cut line runs along the edges of the wood pieces.
Tap the excess portion of the slate with the hammer to break off the extra slate.
Drive an S-hook between the two slates just below the damaged area on the roof with a hammer. The S-hook will hold the bottom of the new slate in place.
Lift the slate piece located directly above the damaged area gently and slide the new slate piece underneath the lifted piece. Ensure that the bottom of the new slate rests securely in the S-hook.