Back Squats

The absolute most important exercise. The squat uses more muscles than any other move. The second most vital exercise is the Deadlift, in which you hold the bar at your waist, yet in the squat, the bar rests above your back, crushing your entire body. I have found the squat to be the most complex exercise in my routine. You should be able to squat your own weight (1x bw) even as a beginner. Here are the points that I find are the most important:

1/ Bar position - High Bar Position is when the bar is above your shoulders and is resting on your traps.This is a position better for having a more vertical torso like emphasizing quads. Low Bar Position is having the bar tucked behind and under your deltoids (shoulders). It promotes a more forward lean for the torso, and emphasizes the posterior chain (hamstrings, glutes, calves, lower back). You can lift heavier in low-bar position. The glutes are the strongest muscle in the body.
2/ Stance (feet width distance) - A narrow stance targets the quads, while a wider stance hits the adductors and is in a better position to hit the posterior chain.
3/ Grip (hand width distance) - Too narrow a grip can cause arm pain and can unbalance you. Too wide may also unbalance you and prevent a tight enough squeeze in your back.
4/ Down Position Depth - Too high will put tension on the knees. Going to parallel is good, and just a little lower is the sweet spot of hitting the stretch for the quads.
5/ Torso Position - A vertical torso would put more pressure on the quads, whereas a horizontal torso would help you sit back more, using the posterior chain.

Eyes should be looking downwards, and worse straight ahead, but never look up as it throws off your spine and puts your neck at a bad angle. You should focus on contracting your leg muscles in the down position of the squat. Take a breath before performing. Don't breathe during the squat. Push your feet downwards and apart as if spreading something. Come out of the hole by rising your hips and back at the same speed. Beginners often rise their backs before their hips, and this causes the exercise to resemble a Good Morning. It's dangerous to perform Good Mornings with heavy weight as you would a squat, so you'll back will be injured quickly. I don't see it taught often, but the squat should be performed powerfully. Sit into the down position, below parallel, and rise upward and extend your hips in a lockout. The squat and deadlift are very hip dominant. The squat being more knee dominant.

Squat in different rep ranges to fully understand the exercise. 20 rep squats make you breathe hard, having an endurance trait, while having a long period of muscle under tension. I'm currently doing 15 rep, 12 rep, 8 rep, and 3 sets of 6 reps.