If you aren’t sure where to go when you step onto an ice or roller rink, this handy guide will help you out. Traffic flows in one direction (usually counterclockwise), with the center reserved for people to work on their skills.
You don’t have to be an expert to go into the center, either. It’s just the place to be if you’re practicing a move other than plain old forward skating. Showoffs might be doing spins and jumps, but you can just as easily use that space to slow down and practice stopping or turning around. Because you’re in a quiet spot, faster skaters won’t have to dodge around you.
Back out in the flow of traffic (which this graphic is calling the “glide lane”), good etiquette means you shouldn’t stop suddenly, cut across the lane, or skate clockwise if everybody else is going counterclockwise. If you fall, stay safe by getting up as soon as you can. This graphic comes from a roller rink, but I skate both ways and can confirm: these rules apply to ice rinks too.