Unless some part is really deep I do it one pass. You are usually going pretty slowly and probably at most 1/2" deep. Kind of anchor your router hand down onto the piece and use the free hand to make small arcs for best control. Smaller routers are easier to handle. There are several bits that are the most commonly used. A 90* vee point for fine detail and sharp corners, a 60* with a flat bottom for flat backgrounds are probably the most common.
Someone I consider a master woodworker once told me that a master woodworker is not someone who never makes mistakes. He is someone who is able to cover them up so that no one can tell.