There are many ways to kill plants. The best way for moss is usually try to dry out the place that it grows since in likes growing in damp places. If that is not an option I would probably suggest salt as a way if you want to do it without harsh chemicals if you don't mind chemicals just use roundup or an equivalent total vegetation killer.

Johndoe is right about drying the area out or you can expose it to sun to keep it from returning, but a bleach solution will kill it. You don't have to go crazy with the bleach, it won't take much, but don't plan on growing anything else, either. It makes the soil incredibly alkalai.

consider growing a moss garden. They can be beautiful. google it.

If you dont change the condition where the moss grows: shady, damp it will return within a year, usually regenerating over winter. I am afraid this a problem that will remain.