When sanding spindles on the lathe, I usually fold a half sheet of sandpaper several times and hold it against the wood. Folding it several times makes it thicker and keeps the heat away from my hands longer. For fine details, I sometimes use a thin strip to get into tight places. I generally work my way through either 280 or 320 grit and 0000 steel wool. Between the last two grits, I often wet the wood to raise the grain. I also reverse my lathe and sand the opposite direction each time I change grits.
As for touching the wood w/ your bare hand, I try not to but only because it gets too hot to touch. As long as it's smooth, it usually isn't a problem.
I don't know if this is the right way; just the way I've always done it.
Bill