Kryogen,
You have received a variety of methods any of which will work. I dry mine at least over night after rolling the brass back and forth in a towel. One other thing I do that will dry rifle brass in less than in an hour - After drying the brass in a towel, I use a tiny bit of Imperial Sizing Wax to lube the brass as prep. for the sizing die. After sizing, to remove the lube residue, I put the brass in a coffee can, cover them with Coleman fuel (naptha gas), replace the plastic lid on the can, shake them for a moment then drain off the fuel. The sized brass is then dumped out in a cardboard tray to dry. Takes less than an hour to dry. Unless you are in a hurry to reload, it's best to just let them dry for a few days. Be sure to separate each piece of brass so that the mouth and primer pocket aren't blocked from access to air.