Small amounts of moss on asphalt shingles?
Moss is there for a reason. It grows because there is moisture. Typically overhanging tree limbs and shade are the problem. You want to cut back the branches over the house so that your roof will get sufficient sunlight and airflow to dry out.
Once you do that, a good stiff push broom should be sufficient to scrub off the moss from those shingles.
Check for roof damage. That moisture is a killer. It is possible that you will need to replace shingles, or even the wood underneath. You may also have venting problems, preventing the roof from properly drying out.
Finally, once you ensure that the roof can dry out, and remove the moss which helps to keep it moist, and replace/repair any problems, you can then add zinc strips to the top of your roof to help retard moss from returning. The zinc leaches out gradually with rain, retarding new moss or algae from growing on your shingles.
Nothing will work unless you dry out the roof and keep it dry though.