1. Your feet should not be pointing straight ahead while squatting, regardless of stance width. This is by far and away the biggest noob mistake. Most people never hit depth / develop knee pain because they squat with their feet straight forward. You should set up with your feet rotated ~30 degrees outwards from parallel (ie your feet should be forming a V with the vertex behind you).
2. When you are squatting down, you should project your knees in the direction that your feet are pointing. Your knees should be out over your feet at all times. Your knees should not go straight forward.
3. Squat (and really all other powerlifting movements) are full body exercises. Your core should be tight; your back should be tight; etc
4. Don't squat in running shoes. If you must squat in running shoes, use a board as the OP stated. Running shoes tend to have a very squishy sole which is great for running but not so great when you are trying to establish a stable base to balance on and push off of. Try to squat in shoes with a hard sole.