This is one of the first questions almost every new bookbinding student asks, and my answer is often a shrug. We're talking about folding sections: no matter how hard you press with a bone folder, you won't convince the paper to go all the way flat and stay flat at that spine fold without a bit of muscle in the form of a nipping or standing press. "Until it's flat when you take it out," I say. If you don't get the spine folds to lie flat, you often end up sewing the book too loose, and you'll have problems later. They look at me expectantly. "An hour? A day?" I shrug.
And so I give you some very very lax folding experiments, for a visual of what kind of change you might expect over what kind of time. (I sort of want to do this properly now, and measure the change in swell, and use different papers to see, and measure the amount of force exerted by my press, but I'm not sure how much I'd get made fun of for that.)
Here's the unpressed textblock below (folded with a bone folder); it wouldn't even stay stacked so I had to use a weight at the fore-edge to get this image. This is 120 gsm Conquerer, 4 bifolia per section, grain parallel to the spine. You can expect a sharper initial fold for thinner paper, fewer bifolia per section, and with grain parallel to the spine, and the overall swell of the textblock will be less with fewer sections.
In order to press the textblock, you can put weights on top, preferably with a board inbetween to avoid impressions, or you can put it in a press. It needs to be perfectly lined up so that all the folds receive pressure and so that you don't get any indentations. If your textblock is particularly bouncy, it will be hard to get it stacked like this, so you might find it helps either to flip half of it (so you have one stack, but half the folds are on one side and half are on the other), or to separate it into a few stacks.
If you use a weight for pressure, use as heavy a weight as you can manage! I don't have a photo handy but when I mean business I have two cast iron 56 pound weights which I painted to make sure no iron will ever get in contact with an object (leaving a mark or a rust stain if damp) and they also have felt bottoms so they don't scratch the boards I put under them. The weights shown below are boxes I made around lead type scraps, covered with cloth and with felt bottoms. If I'm not in a rush I usually weigh down springy textblocks like this for a little bit before I try to press them properly, just to make it a little easier to get in the press. Using a smaller weight lets you actually hold the textblock in place while you apply the pressure, whereas once it's in the press, you can't really get your fingers around it. These would never apply enough pressure on their own to get the spines really flat, but they'd be better than nothing, of course.
Have access to a press? A big one? Have a lot of textblocks to press? You can press as many as you can stack and lay side-by-side while still keeping the stacks tidy. You can make a book/board/book/board sandwich until it's too heavy to carry. (Again, though, for more springy textblocks, probably one layer is more manageable as the more you add, the harder it is to press everything without something moving.) Go easy on the press as you screw it down, because you don't want everything to shake and get out of alignment in your enthusiasm for pressing. Do you see how mine are a little out of perfect alignment in the second photo below? I went for it, because I couldn't get them straight the first time, and after an hour or so I took them out again and squared them up properly since some of the air had been knocked out and it was easier.
The textblocks below have been pressed for an hour, a day, and a week. I left them in there for three weeks, I think, to get them perfectly flat—the answer to the question is "as long as you can."