Burning thigh muscles and fatigued glutes come standard on the leg press machine, but knee pain shouldn't.
If your knees hurt while using the machine, one of three things is happening: You have an injury that's causing the pain; your technique is off; or the leg press machine isn't properly adjusted to fit your body.
Be Mindful of Injuries
Knee pain accompanied by swelling or that involves sharp pain indicates an injury, and that it's time to see a doctor. If you experience the pain during other activities, such as running or stair climbing, also suggest injury.
A knee injury doesn't mean you can't use the leg press ever, but you may need to wait for your issue to heal before getting on the machine.
Technique and machine-adjustment issues are usually less worrisome and can be solved relatively easily.
Double-check your positioning inside the machine: Your hips and back should rest against the back of the seat. Adjust the weight sled -- and your foot position -- so that when your feet are flat on the sled and your knees bent at about 90 degrees, your knees don't completely obscure your view of your big toes.
Double-check that your toes and knees are both pointing in the same direction. If your toes go one way and your knees the other, your knees have good reason to hurt. Finally, don't lock your knees when your legs are at full extension.
If these fixes don't work, or you just can't seem to get the form right on your own, consult a trainer to help with your alignment. You may need to focus on pushing with your heels, rather than the ball of your foot, to activate your glutes or start with lighter weight.