How often should my troops use Overwatch?

When my troops are deployed on a mission, how often per turn should I use the Overwatch command? Are there particular classes that are better at this, or is each class equally useful in this regard?

I'm new to both XCOM and turn-based strategy games, and I'm having a tough time keeping my guys alive, even on the easy difficulty. I think my main problem is that I'm being too aggressive in trying to explore the map (my guys typically spend each half turn moving). Is Overwatch something I should be focusing more on?