Ok so, I think the guys have already covered conditioning and supplementation pretty well. What I want to explore further is mobility and form.
Let's start from a fairly extreme premise that; if we are able to sit into a full body-weight squat every day for a month without a problem then, as long as we give ourselves time to build up work capacity, we would be able to add weight to that.
Obviously at some point you will run into recovery problems and life get's in the way. However I'm pointing that out to say that as long as you're not hurting yourself it's just a matter of adaption.
So onto the first problem; how do we not hurt ourselves?
Involved in the squat are around 4 big joints and/or points of flexion. Ankles, Knees, Hips, Upper back. Each of these can produce mobility and flexibility problems. Consider also that each of these areas can interact with the other to produce a seemingly endless supply of additional problems.
So how to start? Well instead of the usual advice of looking at your own squat and trying to fix it, what I've found helpful is to look at someone else who's built like you and squats like you want to squat and then try and get into those positions. For me it's this guy seen here squatting a fairly casual 800lbs+ weighing 180lbs:
He has the relatively long femurs, but manages to get his knees both out and forward enough to slot into the hole. This allows him to keep his torso upright which takes advantage of the suit and is just generally a nicer style.
Looking at his ankles, he has enough flexibility and stability to allow movement of the shins out and away from his ankles. I think this is a key area, if flexibility isn't there then it will actually have a knock on effect by not allowing the hips to come forward and result in forward lean of the torso.
If you're going to depth there has to be enough strength in the quads to support the knees tracking past vertical. This goes out of the window if you have short femurs, a short femur'd lifter can basically just take the piss with their form and still hit parallel. For the majority of us though forward knee travel is a must.
If this isn't allowed to happen then the hips must move back in order to compensate, again resulting in forward lean of the torso assuming proper depth.
Sufficient flexibility is required here to allow for the knees to be pushed out enough and for the lower back not to round. This isn't the most stubborn area, and some quick, deep front squats or jump squats can increase mobility here quickly.
Another vital area. Strength in the thoracic region will allow a lifter to keep his chest up. Assuming poor thoracic flexibility and strength, all the rest of the flexibility/mobility work will be made useless as the chest will still slump downward. Upper back flexibility and strength is essential to keeping a relatively upright squat.
Even all that is just touching the surface of good squat form. As I said at the beginning find someone who is built like you, use that as a teaching tool for where your body should be and work on the 4 specific areas to allow you to hit those positions.
There are plenty of websites for specific stretching but without knowing what you're going to stretch they are useless.