How do you know who's turn it is in golf?

You don't really. At least, not when you tee off. Once you are in the fairway, whoever is farthest from the hole, or green, usually is next.

Let's say you are playing Golf and are playing against one other person. You both tee off, in no predetermined order, and arrive at the fairway. If your opponent out drove you, hit his/her golf ball farther than yours, then it is your turn next. After you hit, it will be your opponent's turn to hit. You keep alternating like this (or if your opponent's ball didn't go farther than your ball any of the times he/she hit, he/she still gets to hit until the go past your ball) until you each sink the ball into the cup.