Having worn contacts for years before, it's simply a matter of two things.
One: Become comfortable with sticking your finger in your eye. Anyone with contacts can poke their eye for a dollar. And squeezing down on your eye.
Two: know what an inside out contact looks like, and how to flip it. The difference in direction could mean the difference between a couple seconds of annoyance, and minutes of excruciating pain.
(I wear glasses for now, contacts only when I need to)