With the lack of attic ventilation in garages, the heat buildup in the roof is even higher. What actually happens is the granules covering the shingles come loose in the high heat. One purpose of the granules is to reflect the damaging ultraviolet rays. When they are gone or thin, the shingle material underneath degrades quickly.
Since your roof is already 20 years old and it is over the garage, I would recommend you install an entire roof rather than try to repair the leaks. Some additional damage will be done just walking around on the roof attempting to find the sources of the leaks. Once you find them, if you can, you will have to disturb old shingles near the repair areas. This can result in additional leaks.
Tearing the old shingles off is the most difficult part of re-roofing a house. Laying the new shingles is actually a pretty straightforward, simple job for most homeowners. The most difficult part of the job is handling the heavy bundles of shingles and keeping your balance on the roof.
With a roof as old as yours, you may be able to lay a new layer of shingles over the old ones. This is commonly done to save money, and it works very well. The key to a good job is making sure the old shingles are not crumbling and the edges are not badly curled. If they are, the new shingles will not lie flat enough over the old ones. Also check your local building codes about re-roofing.
Take all the appropriate safety precautions when working up on any roof, even a relatively low one. Don’t work alone, and always have your cellphone with you. Even if you do not fall off the roof, you may get caught in an unbalanced position and need assistance.
Only work on a roof when it is dry, and wear soft-soled shoes for greater traction. It may be overkill, but I prefer to use some mountain climbing gear (rope, harness, repelling equipment) and tie myself to the chimney or a tree. It is not too cumbersome, and it allows you to let yourself down slowly to the ground, should you accidentally slip.
The shingles are overlapped on the roof, so gravity carries the water from one over the next. There is quite a large overlap, so wind-driven rain does not back up under the shingles and get into the garage.
To make sure you have the shingles in a straight line, snap chalk line first along the roof. Don’t just try to eyeball it, or it surely will end up looking like a do-it-yourself job. Using a nail gun makes the job much faster, but a hammer still works well for shingles. Carefully flash around a chimney or valley.