I use a sheet of glass at an angle over an extra photo tray to help me squeegie off the water as prints come out of the rinse. First I do the back, then lift the print and while holding it up, run the squeegie down the empty glass to clean it. Then the print goes down on the glass face up and I squeegie (lightly) again. Don't worry about getting it bone dry here. A few drops make no difference.
Next I have a set of drying screens (keep them clean). I put the prints down FACE UP for a while. I know the recommendation is FB face down and RC face up but I've had some problems with soft emulsion taking on the screen patter. If I leave them FACE UP for an hour or so then turn them over it seems much better.
After a day on the rack (no forced air drying in my case) they will have curled up a bit. In the winter less so but the summer can be quite humid even with my air conditioner running. At this point I use a dry mount press to flatten them. I use sheets of 2-ply matte board above and below the print. The press is on its lowest setting. Each print gets about 20 seconds in the press then out. I repeat this a few times. If the matte board seems damp I switch it for a fresh set. Always seem to have some extra pieces lying about.
So far this has worked fine. Haven't trashed a print yet (knock on wood) and I try to be very careful about washing the prints and cleaning the drying screens so I'm not worried about contaminating the matte board. Also check the matte board once in a while to make sure something hasn't gotten stuck to it. If you press it with some filth in there, it will make dent in the print.
Here is my procedure. My climate is very dry so left to their own many prints will curl until their corners touch.
1. I dry them between two clean screens. This has never left a mark. They come out flat with a bit of wave. This part is important as trying to press a seriously curly print often damages some emulsions by cracking it, especially the corners.
2. After they are dry I put them in a hot press and then pull it from the the press and let it cool under some books. The cooling part is important, because if the print is allowed to cool without being held flat, it will have a tendency to get back a little of its curl. By doing this they come out as flat as can be. On occasion if I don't mount them, they will curl back up very slightly. Mounting, or another session in the press cures that.
I use my wife's clothes iron to flatten my fiber paper. I place the print face down between 2 pieces of 3 ply matt paper. The iron is set as high as it can, without steam, and then just move it up & down, left & right again, again and again until it's flat. Maybe 5 - 10 minutes. I then lay a large heavy book over the matt paper and let it cool down. I only use the matt paper for drying... nothing else. On the back sides of the matt paper I wrote down "backside only" so I don't have dirt or dust on the side that touches the fiber paper, I also store the matt paper in a bag so I don't try to use it except for flatting my print.
I always start the same way: let the FB print air dry, but not bone-dry.
First method I tried was to use a clothes iron. By sandwiching the print between two sheets of watercolor paper, I could "iron" the print to dryness and reasonable flatness. On the plus side, it's manual labour, which can help to free your mind from worries. On the minus side, you'll spend forever drying your prints if you have a stack of them.
Now what I do is simply put the prints between sheets of acid-free blotting paper, and put a few books on top of them. Every once in a while, I let the prints air a little bit, then it's back to the blotters. Eventually the prints are pleasantly dry and flat, after a day or two. But they will always curl a little bit no matter what, unless you mount them.
The paper brand makes a huge difference. Anything remotely Eastern European will curl a lot, whereas Ilford and Kentmere stay flat even without any pressure.
Maybe I missed something, but I'm surprised that I haven't found any mention of the method we use quite often here in this part of the world. After washing, put the print face up on a plate of glass (with appropriate thickness) and fix the border with an adhesive tape, the whole perimeter, about 5mm on the print should be sufficient. It must be the old fashioned brown paper tape which is usually licked to get wet (or passed over a wet sponge, but do not wet it too much). Let the whole thing dry until the next day (don't hurry too much) and then cut the print with the stuck tape from the glass and then cut off the border strip with the tape (or hide it under a passe-partout). Especially with "F" papers the surface will get a very nice smooth look and will be perfectly flat.
The forces which try to contract the print when drying may be quite big with large prints, that's why the glass should be thick enough (5mm for 30 x40 cm will do).
Here, in my strange country, where I don't know if we even have name for a dry mount press, we dry our fb prints using sheets of glass and paper tape with water glue.
In short: put a wet print on glass sheet, squeegee it, and stick to the glass with the tape along all borders. Leave overnight, cut the print with a knife.
I've actually never seen that described in english. Is it something local?
I use Mortensen's method, which is to grasp the face-up damp print and pull it down over the edge of my table. This will take the curl out of fiber paper.
Also agree with rwyoung.
I also have only 11x14 heat press. For 16x20 prints I sandwich one at a time between 2 sheets of 4-ply acid free board and set the dial to about 175 degrees and press sometimes for up to a full minute. I first heat press the middle area and then go around and press each 1/4 section which will overlap each other.
With these, as with smaller sizes, I place the sandwich right out of the press under a 21 x 18 x 1/2 inch sheet of glass. This is quite heavy enough for a single print sandwich. While this is cooling under the weight, I continue to heat press the next print. Then take the previous one from under the glass and place the next one from the press under the glass. This sets up a sort of assembly line - while one is cooling, one is heating and so on and so on.
If I end up with several prints, I'll stack then together under the glass with books on top for hours or overnight.