The quads are probably the single strongest group of muscles on the human body. As such, they respond well to heavy weight and are capable of termendous growth once you start to train them properly.
No one will ever forget Tom Platz and it will probably be a while before anyone acheives the other-wordly quad development he possesed. His mentality about training legs pushed his quad development well past that of even todays Olympia competitors. Essentially, he worked like a wild beast very time he hit legs. Squats, leg presses, leg extensions until his legs were barely able to twitch followed by an hour or more of hard bike riding.
Because of the way Tom Paltz prioritized his workouts around legs days, he grew disproportional and had to make major adjustments to get his upper body to the same level.
Most young lifters today have exactly the opposite problem. Underdeveloped legs in comparison to the rest of the physique. If this is you, you'd better think hard about reorganizing you schedule around legs so that you hit them first thing after you've come back from your off day. If you've never trained legs, consider this: judges aren't the only ones who look at leg development. Wether the reader is male or female, I can't stress enough the appeal to the opposite sex of well developped legs.
On to the exercises...
Rest the bar on your trapezius muscle and use a grip only slightly wider than your shoulders to safely keep the bar in place. Flex your trapezius as best you can by rolling your shoulders slightly back. This padding will help distribute the weight of the bar a little better.
Feet positioning is more important during this exercise than any other. Choose a stance that is a little wider than should width with your toes pointed slightly outward. I submit that you can isolate different parts of the quads with different foot positions, but this particular stance is the best--and safest--for overall quad development.
Performing this without a spotter and a weight belt is like driving a car without a seat belt--or brakes. Don't.
Unrack the weight square your shoulders. Your weight should be evenly distributed over both feet. Crank you head back slightly so that you are looking a few degrees above normal eye-level. Keep a slighy arch in your back as you begin to squat down.
Bend your legs and lower yourself until your upper thighs are just a hair below parallel with the ground. Some lifters advocate the "full squat" which entails going so far down your butt nearly touches the ground. Most of us lack the hamstring and glute flexibility for it so I'll leave it there--Achim Albrecht has two of the largest qudas in the pro ranks and he performs full squats which is reason enough to think about doing them if you are able.
Be sure not to squat down to quickly or you'll be unable slow the weight and reverse direction. I can actually handle more weight if I perform the reps slowly and deliberately than if I try and execute the reps more quickly.
At the bottom of the movement, keeping your back slighly arched, your head up and your shoulders square, drive the weight upward until your legs are just slightly bent. Don't lock you legs unless you want to pick up your knee-caps after the set.
Quadraceps, glutes, hamstrings, trapezius.
This exercise is really hard, but it is basically the single best mass-builder next to perhaps deadlifts. Definitely make it part of your regular quad workout.
If you don't have a spotter or you feel uncomfortable with that much weight on your shoudlers, try the smith machine. It is a very safe apparatus and it gives you essentially the same workout. Remember, though, because of the way it is built, the bar on the smith machine is only 15 lbs. compared with 45 lbs. for a normal free weight bar.
A lot of people wrap a towel around the bar or put a special pad on it to help cushion the weight. This is an especially good idea if your not fond of big red lines on the nape of your neck.
Hack squats are performed on a machine similar to the leg press. The weight rests on a carriage with shoulder and back pads. With your back to the machine, put your feet on the platform and your shoulders under the pads. Start in a standing position and squat as far down as you are able. Push up and repeat.
Quads, emphasis on upper quads.
This is a really good exercise for developing the sweep of the upper thigh. Because it is so intense, I don't recommend doing it in the same workout as squats. Pick one each week and go all out with it--you won't be able to devote yourself 110% to squats if you know you've got three drop sets of hack squats coming up.
This is one of the most worthwhile machine exercises. Be sure to keep your butt on the seat and fully extend your leg, briefly holding in the locked position before slowly lowering the weight. Controlling the weight during the negative portion of the rep is especially important during this movement to get the biggest burn possible
Quads.
This exercise goes equally well at the beginning of your workout as at the end. If you do it first, use it to preexhaust your quads so that squats and leg presses will be nothing less than brutal. If you do them last, perform them as a burn-out exercise to squeeze every last drop of energy from your legs after a hard workout.
The key to getting a lot out of this movement is to control the weight on the way down and to lower it as far as possible without rolling your lower back off the seat. You will find you can move more weight in this exercise than in any other.
Choose a foot position so that your knees do not buckle inward or at the bottom of the rep. I like to put my feet shoulder width apart on the top half of the platform with my toes pointed a little outward. The important thing is to choose a position that allows you to generate the most power while maintaining rigidly strict form.
Quads, hamstring, glutes.
Because you can move so much weight, I perform this movement as a mass builder taking my reps from 15 downto 6 in the last set.