If it's mold / mildew, take 1 cup of household bleach and mix it with 1 gallon of water. That's the ratio. Use a brush, a broom, or whatever and start scrubbing. Let it sit a few minutes to loosen up the stuff.
What you might want to consider is a low powered, power wash. It's less work and much quicker. In BOTH cases, do the entire roof because you will see color differences if you only do the affected area. Try to avoid having the water run down the rake edges of the roof line because it might streak and/or stain your siding. By keeping the water on the roof, it can run into your gutters.
One parting thought. You might want to address the cause of the problem. If you have overhanging trees that obstruct air and sun, prune them back. Mold and mildew florish in conditions where the little air movement, dampness, and little to no sun.