It's probably not surprising that, when the majority of men can't even be bothered to wear a tie, almost noone still wears pocket squares. It is a great shame though, since this is one of your best opportunities to wear the sort of fabrics and patterns that would be impossible on a shirt or suit and sometimes even too flamboyent for a tie. The key is that you can show as little or as much of your pocket square as you want. If you're wearing a particularly colourful silk pocket square, there's no need to have acres of it falling out of your pocket (unless you really want to). A small fold peeking out of your pocket is generally much more elegant and less attention-grabbing. And of course, if in doubt, a plain white handkerchief always looks smart.
A lot of places on line will show you how to fold a pocket square in a number of different ways, which is fine, but I'm not generally a fan of folds that are too precise and perfect. You're much better off just stuffing it into your pocket with either the points or the middle showing, and then rearrange it until you're happy. As long as it fills the pocket fairly well, it'll pretty much stay where it is and you can forget about it. Until someone compliments you on how smart you look.