Wes gives an excellent description of the 20 rep breathing squat.
Might add a few points to this protocol. There are two versions of breathing squats. First is using a lighter weight, 100lbs or so, keeping this weight for all future workouts. Mark Berry developed this system probably 80-90 years ago. Second method is adding weight (usually 2 1/2's) each workout, working up to some impressive weight after a while. J. C. Hise (best I know) developed this system. If new to trying breathing squats, might suggest a light weight (100lb) to become accustomed to the breathing and the higher reps. Either light or heavy, both can give results, depending of the level of development desired.
You breath through the mouth (never the nose) heavily, expanding the upper chest with air. Another reason to use a light weight is to get use to the breathing pattern, some can become dizzy with a heavier weight at first. Take about 3 to 4 workout to get use to the breathing and style of the squat. Than begin adding weight.
Do a set of light straight arm pullovers (20 reps) after a set of squats. Suck in as much air as you can. If your young enough (mean average 24 years) the cartilage has not matured and set to a harden state. Which means that a rib box expansion (to the chest) can be expected. 1 to 2 inches gain in over all chest measurements are common (expect more in some people). The breast bone can become sore, during and after a hard set of breathing squats (even days after). Take advantage of this stretch by adding the pullover right after for an even more stretch. (this is not bone growth or enlargement but the cartilage between the ribs themselves..which some get confused with)
Breathing squats are a form of the Rest/Pause system. You will be taking 5 to 8 deep breaths during the last part of the set. Take as many breath/rest between reps as you need, just make the goal of 20. Some hit 30 or more reps per set. Going to find that this form of squatting becomes more of a 50-50 physical and mental effort. Only do one set of squats, if done correctly that is all that is needed. Just to note,you may be praying for death after the 18 rep but keep on going. Suggest doing these in a PR/cage or have a couple of guy's stand by. Add 2 sets of benches, presses & row..that's it. Try 2 times a week workout, to see how the body adjust.
When I began training ,with serious intent, at 16 I gained just about 30lbs in 8 weeks. And lost around my waist. The chest/rib box gained quite well also. Polynesian genetic do help, but many a football player has gained 10 to 25 lbs in a somewhat short period of time with this style training protocol.
Some have applied this method to DL's. I have use it with cleans (PR or floor) and found it an exceptional movement. Even have done the pullover (bent arm) in this breathing style an had gotten surprising good results, like lats, triceps and chest. The pullover is the upper body squat, as Jones suggest years ago. Good Luck.