Nothing much to add to what's been said above, apart from i can verify it is the truth. I've had a lot of knee problems (rebuilt ligaments, then damaged meniscus), and squats really seemed to be a major part of recovery towards normal levels.
I find a bit of light cycling and a few gentle air squats very good if my knee is sore or puffy from a previous hard workout, and I tend to ice it after a hard bout to prevent puffiness.
Also, you sound a bit keen, like me and everyone else on this site, but take it easy if your knee is sore. I know from experience that if your supporting muscles are tired they offer much less resistance in the case of a fall (or slip in the shower in my case). In the early days, i used to exercise then put on a knee brace for additional support afterwards.
I take fish oil, glucosamine, chronditin (i think that's the spelling) and manganese supplements, which seem to help. I've been told to avoid dairy, but i've not really noticed a difference with that.