Your mirrors are there for a reason so use them. But understand their limitations and advantages first. Every vehicle has blind spots - areas behind and around you that you can't see into because of the design and position of the windows and mirrors. You can minimise the size of these blind spots by adjusting your mirrors properly - and again this is something that most drivers will find hard to do and even harder to use to start with. Most drivers have their external rear view mirrors adjusted so they can see some of the rear of the car in them. Wrong. Doing this creates the biggest blind spots. To adjust them properly, do this. If you're in a left-hand-drive car, sit in the driver's seat and tilt your head as far to the left as you can - so you're resting on the window. Don't lean your body - just your head. Look in the left external mirror and adjust it so you can just see a little bit of the rear of your car. Now when you sit upright again, in your left mirror, you won't be able to see any of the rear of your own car. Do the same for the right mirror, but tilt your head to the right so your cheek is resting on your shoulder. If you do this properly, as a vehicle passes you on either side, you should be able to see the nose of it in the side rear view mirrors just as the tail end of it disappears from your center mirror. Voila - tiny blind spots. Now this never excuses you for not double-checking. Every motorcyclist is trained to do head-checks and as a car driver you really ought to do the same. If you check your mirrors and you're not 100% sure, do a quick over-the-shoulder check before turning or changing lanes. If more people did this by habit, there would be a lot less side-swipe accidents.
The last thing to know about mirrors is how you drive when you're behind a larger vehicle. It's really super simple. If you can't see the mirrors of the truck in front of you, he can't see you following him. (Plus it means you're way the hell too close to him). Fall back - make sure you can see one if not both of his external rear view mirrors. It gives you more chance to anticipate his moves, and it gives him more chance of seeing you.