Pry out the roofing nails with a pry bar.
Wiggle the torn shingle free of the surrounding shingles, trying to keep from brushing the top surface against other shingles, since contact can disrupt the sand embedded in the shingle's tar.
Cut the felt paper with a carpenter's razor into a rectangle equal in shape and size as the entire shingle. Usually used to cover the sub-roofing, felt paper consists of a soft, almost felt-like surface on one side and an adhesive, tar-layered surface on the other side.
Apply horizontal and vertical lines of waterproof caulking to the felt side of the felt paper at approximately 1-inch intervals, using the caulking gun.
Snip the aluminum flashing with tin snips to approximately 1 inch to 2 inches smaller in circumference than the torn shingle.
Spread lines of caulking along the entire bottom surface of the aluminum flashing at approximately 1-inch intervals.
Sandwich the aluminum flashing between the caulking-layered felt paper and the shingle.
Lift up the surrounding shingles.
Slide the repaired shingle back into place.
Fill the tear with two or three 1/4-inch beads of waterproof caulking. Although you have repaired the tear from beneath the shingle, water can still work its way between the tear; thus, you must repair the tear itself.
Spread the waterproof caulking with a plastic putty knife until you have covered the tear with a minimum of 1/2-inch of caulking. The caulking will keep water from penetrating the tear.
Fill the original nail holes with caulking, using the caulking gun.
Nail the shingle back into the roof, placing nails approximately 1 inch to the side of the original holes, using the roofing nails and roofing hammer.