Here is an absolutely terrific exercise for strengthening the quadriceps. This exercise has been the the torture, umm...exercise of choice of many a ski instructor.
I particularly like this as a beginners exercise because it is isometric and therefore the risk of injury thru bad form is limited and it is also a good starting point for some knee rehabilitation programs.
The set up is with your back flat against a wall, knees at 90 degrees and elbows raised in a Cossack style position. Make sure your knees don't bow in, our out (maybe by placing a light ball between the knees - see above).
A good starting point is to hold this for 40 seconds, building up to 70 seconds.
If the sado-masochist in you finds this too easy try it on your tip toes and then on your heels, to hit the calves and tibialis anterior (muscles of the front of the shin).