You saw a picture of some guy on the Internet with a thing in his breast pocket. You thought it looked cool. You bought a pocket square. Now you're staring at it and thinking, “Now what?”
You've gotta get the thing in your pocket somehow. Any method that accomplishes this task is called a pocket square “fold.” There's no precise origami required. In fact, precision is discouraged, for two reasons:
The first rule of pocket square-wearing is that you're supposed to act like it's not that big a deal. As if you didn't just search the Internet for how to wear one. So it should look like you didn't care too much about the fold. A risky, though plausible, method for accomplishing this is to actually not care too much about the fold.
Whatever fold you settle on in front of the mirror, you will have a completely different fold within 5 minutes of walking out the door.
There are two methods for “folding” squares:
The TV Fold The TV fold should be used only if you've got a linen square. Occasionally I see a TV-folded wool square that looks nice, but this is rare. To effect a TV fold, simply fold the square until its width is approximately equal to the width of your pocket, and then longways until only a sliver shows from the pocket. Personally I like to fold mine a tad wider than the pocket so that the square bends just a bit.
Not The TV Fold All other folds are intended to look like you just stuffed the thing in your pocket. This starts with grabbing the square in the center, folding it over itself, and then stuffing it in the pocket. You can stuff it in points down. You can stuff it in points up. You can stuff it with the folds facing sideways. You can stuff it in with the folds facing forward. You can even poke it before you stuff it. Once stuffed, fiddle with it until you're satisfied. I like larger squares, so that I can stuff them in points down, but pull out a couple of them.
For both folds, make the shoulder side slightly higher than the sternum side. This way the square follows the line of the lapel and points towards the shoulder. But it's not that big a deal.