Replacing one or two damaged shingles is a doable repair that stops a small problem from becoming a leak. Work safely on the roof — or hire it out if you're not comfortable at height — and do it in mild weather when shingles are pliable.
Loosen and remove
Shingles are sealed to each other with a tar strip and held by nails hidden under the shingle above. Gently lift the shingles above the damaged one to break the seal, then slide a flat bar under to pop the nails holding the bad shingle. Remove it carefully.
Install the new shingle
Slide the new shingle into place, aligned with the others, and nail it in the proper nail line (where the next course will cover the nails), then re-nail the shingles above. Cold shingles crack, so warm weather or a gentle warming helps them bend without breaking.
Seal it
Add a dab of roofing cement under the new shingle and the tabs above to re-seal them against wind, since you broke the factory seal. Match the shingle colour and type as closely as you can.