"HELP! I can't get below parallel in my squat." and "My heels always come of the floor at the bottom of my squat." seem to be the most common issues I hear about squatting on the internet. For most people, simply sitting in the hole and working out the issue is their best bet; a bottom-up approach. Dan John does this through "goblet squats". Westside does it through box squats.
I approach it by having students stand in front of a chair or a support beam of a power rack and then getting into their bottom position and then shifting their weight onto their heels. Moving the hips and straightening the lower back will help the trainee feel how stress is transfered from the knees and ankles onto the hips and hamstrings. With practice, the trainee will be able to duplicate this position with less effort and with greater stability.