The quickest way to remove moss from sidewalks is with a power sprayer - it is quite satisfying to see the moss flying (all over your house, plants, car etc. so be careful) and your walkways looking pristine. But moss always returns in western Oregon and assuming a permanent move is not in your future, you will have to treat the sidewalks with some sort of substance to deter (but not totally prevent) its return. The following document lists several alternatives and where it is appropriate to use them. As always is the case, keeping up with the moss before it gets too heavy saves time down the road.