We've heard the refrain a thousand times before that the squat is the "King of All Exercises". This gets redundant after a while. There are a myriad of reasons why it's stayed on top for so long, the main one being that it's just the best and you should be doing it.
Here are some helpful tips on squatting:
1. Grip Width Grip the bar with the narrowest grip you can manage without shoulder discomfort. This helps you remain tight throughout the lift.
2. Hand Grip I like taking a full grip on the bar these days. I used a "thumbs-around" grip for the first half of my squatting life. I don't see this as a deal breaker. Don't get too caught up, just pick and know that you can try the other grip at any time.
3. Bar Placement Proper placement of the bar on your back depends on your body type and what's most comfortable. Some people have shoulder issues and can't carry the bar very low. Others just plain suck at high bar squatting. Wasting hours pouring over internet arguments won't give you a solution; find out for yourself. Place the bar where it allows you to reach depth with best form and least discomfort. Understand that the bar placement may change over time.
4. Taking The Bar Out Fill your diaphragm with air before taking the bar out of the rack so that your core feels very tight. Lift the weight out of the rack with purpose and controlled aggression. Never "wimp" the bar out. I like to do this with a single large breath which I won't let out until I'm in my stance. This allows you to begin the lift as the aggressor which works for you both mentally and physically. If you don't control the weight - it controls you.
5. Walking Out The Weight Any more than two or three steps back is a waste of time and energy. Be efficient and in control. I mentally count "One, Two" when taking the bar out to make certain that I only take two steps. If you are newer to squatting, the third step can be added as an adjustment step done with one foot to get the feet are even and at the correct width.
6. Your Stance Hip-width or just outside the hips is good. Similar to choosing your bar placement, place your feet where it allows you to reach depth with best form and least discomfort. When working with athletes you can help them find their footing by telling them to get into position to do a long jump. It's usually their stronger and more comfortable footing. If they suck at jumping this is not a good idea. Start with hip-width and see how it goes. Like your bar placement, your stance will change over time; don't be afraid to adjust.
7. More on Stance Your toes should be pointed out at a 30-45 degree angle. This will allow your knees to track comfortably and correctly.
8. Back Position Arch your upper back for the entire lift; but don't over arch so that you are standing too tall. Again your upper back will change as you get bigger. When I was under 200 pounds, I'd emphasize the upper back arch. Once I got bigger, I just made sure it didn't round. Whatever you do, don't round. A rounded upper back means a round lower back. There are differences in squat style and plenty of do-nothings willing to tell you what's wrong with yours. The most important thing is that your spine is not rounded over and you aren't changing spine position during the lift. If you're not sure what your back is doing while your squatting, you can try focusing on your chest. Keep your chest up, shoulder blades pulled together and sit back and down. Same result of maintaining good back posture. Remember that "chest up" doesn't mean you are straight up/down - it means it's locked in and not folded over.
9. Eyes They need to be focused. Some people believe you should look straight up when you squat. These people are not good to listen to. Your eyes should be directed straight ahead or just slightly downward. Don't take your eyes off the point you choose. Pick something (not someone) and stare intently. Even if there's movement and distractions around this point, it shouldn't affect you. Remain 100% focused. The above clearly excludes staring at yourself in the gym mirror; this is a terrible habit. If the rack is pushed right up to it, focus on the reflection of an object in the background.
10. Your Elbows Keep your elbows down and try to force them under the bar. This will help keep you from rolling the weight towards your neck on the way down and your hips to drive first out of the bottom on the way up. It will also help keep your chest up and prevent you from squatting into your legs first (slumping down with bent knees) instead of your back (sitting back strong with your chest high). On the way up, the first thing to shoot up with many new squatters is their ass and the movement looks more like a Good Morning with their body folded over. Remedy this by pushing with your hips and keeping the elbows under the bar - or at least trying to. A good squat requires that your body moves in unison- not piece by piece.
11. Before The Descent Before the descent, take another breath and go. Keep this air in until your about 2/3 of the way back up. Then you can let it out. I've taught myself to hold my breath for 3 reps but this is very difficult and I wouldn't recommend it for everyone.
12. The Descent When you begin your descent, push your knees out to the sides and your glutes back. Again, not slumping straight down by bending the knees first. This quickly cleans up many ugly squats. If you are sloppy on the way down (or too fast), grip the bar as hard as possible and try to "keep in a huge fart."
13. More On The Descent Your descent should be slow enough to permit you to maintain good form, but it should be fast enough to not waste energy or kill the stretch reflex at the bottom. Many lifters will "dive bomb" their squats. This is a fancy term for dropping very quickly and almost catching the bar in the bottom position before squatting back up. This is okay for advanced lifters who know their bodies and have great technique, but it's probably unacceptable for about 99% of the rest of the population. For younger athletes, I always tell them, "Total control on the descent." At no time should the bar dictate where you go - your body should dictate everything. When you get more experienced and much stronger you will be able to make small adjustments.
14. Get Parallel Descend at least until the tops of your thighs are parallel to the ground. Go deeper if you can but this is the minimum depth you should shoot for. It's also the minimum depth for a good lift in a powerlifting meet. However for athletes and general population lifters you'll get best results from squatting deeper. Whatever you do, don't get depth suggestions from College Lifting Hype Videos. Horrid.
15. At Parallel Once you hit parallel or below, drive your elbows under the bar and explode up.
16. The Bottom Bouncing out of the bottom position or "the hole" is not a bad thing. Losing your air and tightness when you do so is. Don't do that.
17. During The Lift Squeeze the bar hard during the lift. This will help keep your entire body tight.
18. Push The Floor This tip has helped many brand new squatters make more sense of the lift. Think about supporting the weight with your upper body with the main purpose of keeping the upper body locked in place. Then in the bottom position focus on driving through your legs and "pushing the floor away from you" to stand up. This change in perspective can help people use their legs better and avoid being too distracted by the back loading. Just remember that when your legs push don't push so fast that your torso can't follow. Once again, everything in unison.
19. No Dancing When you're going for a personal record, especially a high rep record, never open and close your hands, shuffle your feet or drop or shake your head between reps. I'm amazed at the weird stuff people do when they are under physical stress. Once your feet are placed, they are rooted to the floor. Once your hands are squeezing the bar, don't let go and once you have your stare, never lose focus.
20. It's Your Fault If you can't reach parallel, or do so while keeping your feet flat on the floor, it's either a flexibility/mobility or technique issue. You need to stretch before and between sessions. If you can reach depth with some weights but not others, it's a strength issue. Either way it's your fault and it's your job to show up to the bar physically prepared and using proper training maxes.
For more detailed information on the Squat, Bench, Deadlift, Press and programming your training, checkout out the 5/3/1 Second Edition book.