Pull the damaged shingles away from the roof beginning with the uppermost shingle.
Pry the old shingle nails out of the roof with a pry bar. If the nails are not removed, they could puncture the new shingles.
Patch any damaged roofing paper with roofing cement to prevent water leaks. Apply the roofing cement with a caulking gun.
Position a replacement shingle at the lowest point of the repair area.
Drive 1-inch roofing nails into the shingle just above the tab slots with a hammer.
Install all but the top shingle with nails, working upward.
Apply a bead of roofing cement to the back of the top shingle, just above the horizontal seal line that runs along the length of the shingle.
Lift the shingles just above the repair area gently and then slide the final shingle underneath the overlapping shingle.
Nail the top of the final shingle into place.