I hesitate to give out such advice because it seems that for any running ailment there are a million and one potential causes and the correct treatment varies based on which affects you. But this has genuinely helped me so, here we go.
I used to get very tight quads and hip flexors (especially in my right leg about 36 hours after running), and I'm pretty sure this was the cause of some medial knee pain. I've successfully alleviated this in three ways:
1. I'm more honest with myself about how slow an easy/comfortable run should be. i.e. I do most of my miles slower; we are talking 1:30-2:00/mile slower than my 'fast' pace.
2. Form: When I run, I push my hips forward, engage my abs, and keep my back straight. There's a lot of conflicting information on running form and most of it is very hard to feel while running. These here are things you can feel while you're running, and it should result in more glute and hamstring activation and easier landings.
3. Hamstrings and glutes. This is the big one! I've spent a few months training my hamstring and glute strength. Hamstrings and glutes are antagonists to the hip flexors and quads, so if the strength is imbalanced things don't work well, and, I think, the stronger muscle group ends up taking more of the workload than it should. Modern day life tends to weaken the hamstrings and glutes (with lots of sitting).
My routine looks something like this:
Daily or almost daily, AND pre-running as part of a warm up/activation
Every few days
Deadlifts. If you don't have access to a gym then it's worth getting a pair of dumbbells. A pair of 4kgs is fine for useful (distance) running strength - you will see diminishing returns as you increase weight. Deadlifts will make you sore, so be careful about timing them around running.