In reply to abcdef:
Think of it a little bit like Goldilocks.
Too hot, too cold, just right.
Too hot - you train too much/too hard, the knee pain will come back.
Too cold - you rest , the tissues don;t adapt to the running, so every time you run you will be overdoing it - the pain will come back.
just right - you just so happen to pick the right amount of running/training to do, your tissues adapt to the load, and you become a stronger runner.
Sounds easy - but it obviously isn't...
not only that, but muscles, ligaments, tendons etc. all strengthen at different rates and with different loads being optimal for getting stronger. It is a case of getting it right.
That being said, if there is something pathological going on, no amount of training is going to get it better. Reducing load and starting at a lower level before building it up is the way around it. Which is essentially Rehab, which means finding a good physio.
Also, if you're running around without using Gluteus medius working your knees might end up being painful because your quads are overworking yadda yadda yadda, find a decent physio.
Also, if running downhill makes your knees hurt, get stronger, practice it more. It is NOT "dangerous" to run downhill, it is simply something that needs to be got used to in terms of tissue strength as there is more pressure/weight going through the joints/tissues. Again - goldilocks principle. Practice eccentric loading, practice it faster, then do it one legged, when you can do that, you probably wont have any issues.
But again... if in doubt, see a physio.