How critical to success are these two exercises? I ask because I have some knee issues and I really want to do them, but it hurts. Could I be doing them wrong? How does a person learn to do them correctly?

As far as I know, the keys for these two are keeping your knees over your ankles. You never want them to go forward over your toes during a squat or with your front leg during a lunge. You also want to keep your back straight and your butt sticking out so your weight isn't all up front in your toes but back in your heels.

I don't know if they are "critical" to anything, but I loooove what they are doing to my legs/butt/how much stronger it makes my legs for running. Aliquot is right, the proper form is to make sure your knees never go past your ankles. It feels a little silly but just try to stick your butt out and keep your weight on your heels. I think this might help:

Squat (minus the dumbbell) http://www.bodybuilding.com/exercise.../barbell-squat

Lunge: http://www.bodybuilding.com/exercise...umbbell-lunges

I find them to be critical. I've had knee problems for years and set out to make them strong by walking a lot and then doing some simple leg extensions (sittin in a chair and straightening my legs then bringing down again). I slowly started incorporating lunges and squats into my routine, only a few reps and then gradually increasing. I seem tremendous results.

The woman pictured in my avatar (no that's not me lol!) is Sylvia Weisenberg, my inspiration for a fit body. She has an exercise video called Tonique Fitness. I kid you not, it is a half hour of various lunges and squats. It is the most difficult fitness program I have ever followed. I started off huffing and puffing within the first 10 seconds of the routine. I'm doing better now but I still can't complete the full video and I have to take lots of breaks during. I know that sounds scary but you feel results immediately. It's great for legs and glutes, cardio, and balance. I stop 20 minutes in.

http://toniquefitness.com/dvd.php

Sylwia came out with new Tonique2 and Tonique Mat - it is a killer workout just looked at the previews on total fitness site

I don't have knee issues, but I do have hip and lower back problems. For me, lunges and squats are absolutely critical to keep pain at bay. The stronger the muscles, the less strain on the joints. I do them slowly and don't stretch too far. If I feel pain, it might help to shift my alignment just slightly. Proper technique is essential.

I can never make it to the mat exercises. Twenty minutes into the lunges and squats and I'm done. I wouldn't be surprised if i burned around 500calories during that 20minutes.