How can I get mold and moss off my roof shingles?

I did a lot of online research about this two years ago for our homeowners ociation, and they are very damaging to a roof so you're correct to want to remove them. They spread through the air, so if a neighboring house has them, they can spread to yours. It would be best to do some online research, rather than rely on my memory, but a light-pressure pressure washer (so you don't remove any of the shingles' surface) or garden hose and bleach or similar product to kill the plants. Use only light pressure and never aim the water under the shingles. Several sites warned against hiring pressure washers unfamiliar with washing a roof because too much pressure can damage the roof itself, and to remove any mold/mildew/lichen as soon as possible because they're damaging. Rinse after washing. Because the water will cascade down the side of your house, be sure to rinse house walls, too. Check under eaves, etc., for other spots with the plants. Wet foundation plants before cleaning the roof and rinse afterward to protect them from the chemicals. While you're up there, you can use the pressure washer/hose to clean out gutters and downspouts to maintain them and keep them more effective. There is a lot of information online and I urge you to do the research. I was surprised by what I learned.