On our last trip, we took fabric tote bags and fabric markers...they were a HUGE hit with our nieces. We've seen all kinds of things get signed - decorative plates, tree ornaments, photo frames, mats, shirts...I think they'll pretty much sign anything that sits still long enough!
Apparently the characters have to take a break out of "costume" after a certain period of time (a half hour seems to stick in my mind, but don't quote me). So from what I've been told, the signing can be done during the "break" when they're still working but have to be "offstage". Some might be done in free time, but not necessarily. They do have to practice the signatures and make sure they stay consistent, and this is one way they can get it in, I guess. Just what I've gleaned from talking with former CMs.
It couldn't be easier - just take whatever down to Guest Services (I try and go early in the cruise) and they have a form to fill out. Best thing I've found is the extra large sized ziploc bags - we just throw the items and markers in and we've never had a problem with everything coming back!
Enjoy your cruise!