How do you polish the rims of a yoyo?

Like a DV888 or California? ???

Start by sanding them with 220 grit. Then work your way up past 1000 grit. You can also use some steel wool in there. Then finish it off with metal polish.

also, I unscrew the yoyo and put the axle in my rotary tool (flexible shaft variable speed drill) and spin hakf of the yoyo while I hold the sand paper against it. its faster and comes out more even than doing it by hand. though you do have to be careful how tight you set the chuck so you dont strip the threads. also, its a good idea to slow the drill down if you can before stopping it. I did this to my DV888 and they yoyo half I was working on kept spinning after the drill stopped, and flew off the axle.
also recommend safety glasses and a mask. the little shaving get everywhere.

Do you know have to take out the axle?

You can put the axle into the chuck of the drill and tighten that down. Then all you have to do is unscrew the half from the axle. NOTE that this method can tear up the axle. I highly recommend wrapping the axle with a couple layers of duct-tape first.