Always use the sidewalk. Never walk in the roundabout or to the center island. Cross the street one direction of traffic at a time; the median splitter island is there to provide you with refuge between directions of traffic.
When crossing entry lanes to the roundabout, watch for traffic approaching from the entry lane direction. You have the right-of-way when you are in the crosswalk, but be careful. Make sure that drivers can see you and stop for you.
When crossing exit lanes, watch for cars leaving the roundabout. Some vehicles will use their right turn signals, but most don't. You have the right of way in the crosswalk but proceed carefully.