Cleaning them involved first emptying the large jars they live in using a filtered tube (so they don't get emptied out). Then we swish the water in the jar around (to get them off the sides and pour their environment into a dish. We then put the dish under a microscope and use pipettes to identify the "white stuff" (produced by algae in their environment) and we try to suck up all the big pieces without sucking up any of the tiny baby urchins!
This is HARD! Good pipette control requires a little bit of practise, or you end up sucking up too much, or you end up blowing everything everywhere. I took about 4x as long as a typical cleaner (hey, it's my first time, and I haven't worked with pipettes since high school!), but eventually I started to feel comfortable with identifying what stuff I needed to remove (I don't need to get ALL the white stuff, just the notable pieces) and how to selectively suck some up without catching larvae. Regardless, I still went through the discard dish (that I had transferred the white stuff by pipette to) and rescued about a dozen minuscule urchins (including a few that I don't think I discarded :D).
Anyway, then they went back into their jars (presumably with fresh water). I poked my head at the adult urchins before running away for a meeting, but it was a great morning.