It's like a stop sign entering a busy road. You stay stopped until it's clear. Never mind the impatient people behind you that probably don't know how to use a roundabout as well. People seem to think that you just enter the roundabout without stopping and people in the roundabout have to yield to them. The people in the roundabout have the right of way so they can get out of it and make room for more.
As a non-USA person, the existence of a four-way stop has always baffled me. I think it is the peak of awful road design. I don't think you could make a worse intersection.