I simply turn the plastic just like wood, although it stinks a lot more... so dust collection or simply ventilation is important. I'll echo Tim and Rudy - drill slow (it'll take longer than wood to do a clean job), clear more often than with wood, and if you don't drill wet, let it cool partway through each section. If you don't let the bit cool, you might get some melting. Use a nice sharp bit, too.
The bottoms of the blanks can very easily blow out (even if drilling into wood backing) so what I do is NOT trim to length at first, cut the blank into lengths for both tubes with generous extra on each end, and drill from the center-band edge out. That way the blowout is on the ends you trim off afterwards. Also, drill VERY slowly at the ends, this can minimize the blowout.
I sand just like wood, using micromesh all the way to 12000. I tend to use a nice light touch, but I stay with each grit longer on acrylic than I need to with wood. I sand it dry, but I wipe off the MM pretty often while sanding it.
And finally, Rudy's comments about color are critical and bear repeating. I like markers, as they do not add to width and do not appear to affect glue bonding. But let them dry real well before gluing.