Sounds like your asphalt shingle roof has been marked by blue-green algae or "moss", a typical phenomenon in areas with hot, humid summers. Removing the algae is certainly a DIY project as long as you have the proper gear to reach the affected area safely. Removing the algae from your roof yourself is also dependent on your roof's pitch and design. Removing the algae from your roof requires a ladder or scaffold, and extra rigging.
To remove the algae from your roof, you can either purchase a ready made cleaning/antifungal solution at your local hardware store or home center, or make your own algae remover using one part bleach, three parts water and some tri-sodium phosphate (TSP) for extra cleaning action.
Before you begin the algae removal from your roof, make sure to wet down any plantings around your home's foundation in order to protect them from damage caused by the cleaning solution. Covering them with tarps while you're working will not be enough.
Then head for the roof and use a plastic garden pump sprayer to apply the solution to algae affected areas, letting it sit just as long as is specified by package instructions or, if you've made your own mix, 15 minutes. Then rinse it away using a garden hose.
Do not use a pressure washer to clean algea or moss as it can damage your shingles. If some algae stains remain on your roof, allow the roof to dry completely before making another pass with your cleaning solution. Repeat the rinsing of the landscape plantings once you're done with the roof algae removal.