Pain in the knees while squatting is often from allowing the knees to cave in. One of the best things I have seen for preventing that is learning how to goblet squat and do a few warmup sets of them before doing squats. Here is an article explaining how to do them.
Goblet Squats
Choopa Phil's suggestion regarding knee sleeves is an excellent one. I use Rehband's myself, but there are several excellent choices out there. Having a bad knee myself, I know exactly how important it is to keep them healthy.
While back squats are a great exercise, if you are having knee pain doing them and also want to be able to squat to a lower depth, try doing front squats. Learning how to hold the bar correctly will suck for a while, but that exercise has done more than anything to build up knee and core strength for me. And it is much safer than back squats; if you can't do the rep, dropping the bar from the front is infinitely easier than from the back.
Another suggestion would be to start training the hip hinge movement. True power comes from the posterior chain - the lower back, glutes, and hamstrings. The stronger the hamstrings, the healthier your knees will usually be. Thing is, the main function of the hamstrings is to extend the hips, not to curl the knee. That is why so many lifters experience hamstring problems. You can do deadlifts of some form, cable pull throughs, or kettlebell swings, among others, but make sure to do at least one of them - or do some sprinting - on your leg day.
As for the knee flexion function of the hamstrings, you can try natural glute ham raises
GHR or Swiss ball leg curls.
Leg curls using Swiss ball. You can also do leg curls using furniture sliders as well.
Sliding leg curls.