The leg press can be done lying down or seated, depending on the machine you use. Some machines are destructive to certain body types so you really need to be careful to ensure that your style of leg pressing and your type of machine are not harming your body.
There are several different styles. Both the vertical and 45 degree models can be good for people who have excellent form, no injuries, and are used with caution.
I recommend the leverage style machines like the ones made by Hammer Strength
Proper Positioning
Be sure your shoes have non-slip soles. Some guys prefer to do this exercise in their bare feet.
Make sure you are sitting in the center of the seat.
Place your feet on the middle or higher of the foot plate.
There is less knee stress with higher foot positioning.
If the foot plate is adjustable,set the angle so that you can push through your heels (not the balls) of your feet.
Knee problems will develop if you are not pushing through your heels.
Even a slight change in foot spacing or angle can have a huge impact on knee comfort.
Start with a light weight and a heel spacing of hip width. Keep the inside edge of your feet parallel.
Try adjusting your toe angle slightly and your heel spacing until you find what is most comfortable and natural for you.
Never let your knees buckle in. They need to stay directly over your feet.
Without weight you can find your proper range of motion. Find the depth that causes your lower back to round just slightly off the back support. If you can adjust the machine make it so you can't go more than an inch past your safe maximum depth. If you can't adjust it find or place a marker to let you know when you should stop lowering the weight.
How low you can go will be determined by the style of the machine, and the condition of your knees. The greater the flexion, the less weight required to exhaust your quads, but the greater the knee stress.
If you don't flex your legs far enough you will need to use more weight to exhaust your quads and this could lead to back problems. So the key is to find your balance between stressing your knees and stressing your back.
Keep head straight. Hold machines hand grips. Keep body tight.
Push with heels.
Don't lock legs out. Stop just short of that.
Take at least two second to make the descent.
Your lower back should keep contact with the back support.
At maximum safe depth push out from a stopped position. Don't bounce out.
Other Tips
Never leg press after an intensive dead lift or stiff legged dead lift. You could fatigue your lower back and it won't be an effective stabilizer for the leg press.
Keep reps above 8. If you load up so high that you can't do 8 reps then you are risking damaging your knees and compressing your spine.
Holding your breath can cause headaches, dizziness and blackouts. Inhale on each descent and exhale during every ascent. You can also take several quick breaths while your legs are extended.
Since there are so many potential hazards with this exercise it is imperative that you stay light for a long time while you see how your body is handling the position. If you can not adjust your machine and you are experiencing knee or back pain after this exercise then do not persist with the leg press machine.