Position a chisel against the center of the damaged shingle and strike the chisel with a hammer to split the shingle.
Insert a hacksaw blade underneath the overlapping shingle directly above the damaged shingle and cut through the nail that secures the top of the damaged shingle to the roof, then remove the remaining pieces of the shingle.
Measure the distance between the two adjoining shingles with a measuring tape to determine the starting width of the replacement shingle. Mark this width on the replacement shingle.
Draw a cut line approximately 3/8-inches inside the width lines marked on the new shingle in Step 3. For example, if the distance measured in Step 3 is 5 inches, the total width of the replacement shingle will be 4.25 inches, because an extra 3/8-inches will be trimmed off of each side of the new shingle. The extra 3/8-inches on each side will allow the wood to expand with the weather without damaging the surrounding shingles.
Cut the shingle across both cut lines with a saw.
Apply a dollop of roofing cement to the back of the new shingle and slide the new shingle underneath the overlapping shingle. To ensure it's secure, you can drive a new nail into the end of the overlapping shingle and through the top of the new shingle to replace the previous nail.