You do not need a print shop. A zine is meant to come off the printer you already have, on plain paper, in the next five minutes. There are two kinds of zine here, and only one of them ever needs both sides of the paper.
Everything is on one side of one sheet, so there is nothing to line up and nothing to turn over. Print it the way you would print anything else, in landscape, on plain paper.
Two settings matter. Print at actual size, not scaled to fit the page, so the fold lines land on the paper's real halves and quarters. And if your printer offers double-sided printing, turn it off for this one.
Then fold it. The fold takes three folds and one cut.
Sixteen pages come from two sheets printed on both sides, in portrait, with four pages on each side. Choose double-sided printing and, if it asks, flip on the long edge. That is the normal choice for portrait paper, and it is what makes the backs come out the right way up.
To assemble it: fold each sheet in half, left half onto the right, then in half again, bottom up onto the top. Slide the second sheet inside the first. Staple twice along the folded left edge, which is the spine. Make one scissor cut along the folded bottom edge to free the pages. Sixteen pages, two sheets, one little book.
If the backs come out upside down, the printer flipped on the short edge. Print it again with the long edge chosen.
Plenty will not, and plenty more have a setting nobody can find. You can still make the sixteen page zine. The trick is to print one side of one sheet at a time, and never a stack.
Two things can go wrong, and they look different from each other, so you always know which one it was. If the back printed on top of the front, the sheet went in with the wrong face up; next time put it in the other way up. If the back came out upside down, the sheet was turned top to bottom instead of like a page; turn it the other way. Either mistake costs one sheet, and only the first time.
Pleat does this for you. Choose the setting that says your printer cannot print on both sides and it runs the job one side at a time, tells you when to turn the paper and which way, prints a small mark at the top of each sheet so you cannot lose track, and remembers what your printer did so the second zine just prints.
Ordinary copier paper works and folds cleanly. A slightly heavier paper feels better in the hand and takes a sharper crease. Glossy photo paper cracks along the folds, so keep it for prints that stay flat.
Choose the paper you actually have before you print, in the app or in your layout, and the fold lines will land where the paper folds. Both sizes make the same zine; the pages come out a slightly different shape.
Send the PDF. For the eight page zine ask for one sheet, one side, actual size. For sixteen pages ask for two sheets, double-sided, flipped on the long edge, actual size. Then fold at home.
More: how to fold an 8-page zine · free printable templates · how to make a photo zine · zine layouts and themes.