Crouching in TR is mainly a means of improving aim accuracy.
To crouch, press [C] (default key). Unlike in most first person shooter games crouching in TR is a toggle, this means you press [C] once to crouch and press it again to get back up. There is currently no way to modify this. Also unlike in most first person shooter games in TR you can't move while crouching, only look around (aim). If you try to move, you'll get up.
Crouching greatly improves the weapon accuracy, especially of long-range weapons such as the rifle, DFG, Rocket Launcher, etc. In crouched position your aim accuracy will stabilize much faster than in upright position, as indicated by the reticle.
However, crouching generally does not significantly improve your defenses, unless you crouch behind cover. The smaller profile makes it harder to hit a crouched target, but the fact that it's stationary makes it easier to hit it. The two effects level out, leaving a crouched target with the same defenses as a moving target (but with much better attack accuracy, making it worthwhile to crouch nonetheless!).
Crouching makes a target much more vulnerable to melee attacks, so crouching is not advised when the opponent is in short range.