Well it took about four years for me to get a double bodyweight squat without trying to do that at all (385 competition squat at 190lbs bodyweight). Those first couple years were pretty inconsistent as far as full workouts and good eating goes, but I will say that I made it a point for a long time to squat at least once a week (and still do).
Most of the time I just pyramided up over 3-5 sets to my heaviest weight for something like 4-8 reps for 1 or 2 sets. Once I hit a rep goal (usually 8, but there have been shorter periods of time where I stayed in an 8-12 rep range, or real heavy 3-6, and even a time when I squatted in a 12-15 range) then I would add 5-10lbs and continue on like that.
As far as other lifts go, I would sometimes do leg press (always higher reps), but if anything helped the most it was stiff-leg deadlifts (also always higher reps... I think the last thing I have recorded is 335 for 12 reps from a while ago).
Squatting all on it's own though was easily 90% of the work toward accomplishing double bodyweight, and like I said it's not something I ever thought about either. I'm not a powerlifter, I almost never test "maxes", I just decided to on a whim in a local competition and found that I could do double bodyweight.
Point being, if someone WERE working toward that as a goal, AND eating enough food, AND training more consistently than I did as a teenager, I'm sure they could achieve this in less than the time it took me.
If I were going to give advice, it would be to eat a ton of protein every day and calories to grow on, and keep your training very simple. If I had to do it all over again starting from a few years ago, I would do squats (2 work sets of 4-8), leg press (1 work set of 12-20), stiff-leg deads (1 work set of 10-15), and maybe leg curls... once every 5-7 days.
...which now that I think about it is almost exactly what I did, I just didn't eat enough food. LOL