Lots of techniques listed here, I'll throw mine in.
I hang them back to back from a line, with clips also at the bottom corners, back to back (yes, they leave marks, but I leave enough border that they are covered by the matte). I use plastic clothespins, easier to keep clean than wood. As pointed out, the slower the better. Sometimes in winter, I leave trays of water underneath to encourage humidity in the room. (The drying lines are over the sink.) There are three lines about a foot apart, loaded from the back to the front. I can fill a 16x20 Gravity Works washer with 12 prints and dry them all.
After drying, I sandwich each print in a glassine "folder" (cut up from a roll purchased at an art supply store), then put into the dry mount press, at very low temp, just enough to feel warm, then I turn it off. Take them out the next day. I'm told by framers that you don't even need the heat. If you don't have a press, a single sheet of flat aluminum or some material (or even thick plexiglass would probably work) with the prints under and weight on top.
If you take the prints out and leave them out, they will recurl to some degree, fiber memory, I think someone said. But if you store them, back to back again in a tight container (like a paper pack or box) they should stay flat.
No matter what I do, though, when I go to frame a print, by the time I measure it, cut the matte, and assemble the frame, it has recurled to some extent at the edges. (I don't drymount them - another discussion).