The names for standard book sizes come from the number of times the full sheet is folded. A folio is folded once, and makes two pages. A quarto is folded twice, and makes four pages. An octavo is folded three times, and makes eight pages. And so forth. If you start with the same size paper, the folio will be biggest, the quarto half that size, and the octavo half the size of the quarto. Below will be an octavo.
Of course, the ability to fold down a larger sheet means you can print many pages on that sheet before you fold up and bind, if you’re a 15th century printer, or that you can do it in your living room, if you’re a bookmaker without access to book making equipment like a board chopper.
Unfortunately simply folding results in wrinkles at the edge of the fold. Think about it: if you fold four loose pieces of paper in half in a group, the middle one sticks out more the outer one, because at the fold the outer one has to go around all of those other papers. By the time you get to the last fold in an octavo, the previous folds restrain the movement of the paper, and it will always wrinkle like this:
If, however, you make a few cuts as you go along, you’ll have no wrinkles!
If you missed the bit about folders and knives, you should read that first. As to the paper, the grain direction should be running short for an octavo (think about it—in the end, the folded section will have the grain running long). There’s loads of information about grain direction out there so I’ll skip that for now.
Bring the right side over to the left and match the corners up. Don’t worry about the far side; your paper might not be square anyway. As long as the corner near you is matched, and you begin folding from the edge near you, you’ll have at least one right angle and the rest will correct itself as you go along.
Here my paper is magically creasing itself without the use of a bone folder or even fingers, but you can extrapolate, I’m sure. I usually do about as much as is pictured with my fingers, to get it started, then run the bone folder all the way up and all the way back down to give it a good crease. Use the folder flat! It’s tempting to use the edge—it’s easier to hold, and you probably feel like you’re getting a sharper crease—but quite likely that you’ll stretch the paper fibers too much in the wrong direction if you scrape like that.
Cut the fold just past half of the length by slipping the knife between the two pages. Pull away from the fold and along the length at the same time. It doesn’t quite matter how far you go down except that you need to go at least halfway, so that the edge will be free to move at the fold.
Fold again, same as before, except this time along the bottom edge you have one cut side and one mostly folded side. Bring the folded side over to the cut side, and crease with the bone folder. Now you have a quarto section.
Cut again, same as before.
Octavo! And the grain runs long, parallel to the spine edge.
You can see the cut edges here give you a nice and even fold, and a 90-degree corner between the spine-side of the section and the head (folded side).
Well, almost done. Press the sections, either under a board with a bunch of bricks on top, or in a nipping press if you have one. You can see how springy the unpressed stack looks; if you sewed that textblock, your sewing would likely be loose or uneven, which causes problems later. If you squish the paper down flat, you’re teaching it in advance to sit like you’ll want it to sit once it’s bound, and it will remember that in the binding.