It's not exactly as the above has said.
You should start with your normal 10-RM max and do 20 reps, taking as many breaths as you need to after the first 10 without putting the bar back on the rack until you've finished the set. Normally 2-3 breaths is enough.
You can try different breathing patterns such as 2 breathes in between every rep, etc. There's an article by Jeremy Likness (attach his name to your searches in Google) that describes a bunch of different breathing patterns if you're interested in common approaches. I'm not sure if Super Squats actually outlines a pattern or what it would be.
The basic plan is to cause yourself to hyperventilate, increasing your oxygen consumption, etc. and allowing you to get out more reps. For this reason, never do breathing squats with a light weight as the oxygen debt won't be great enough to compensate for the oxygen you're taking in, which can cause you to pass out. Many people have never reached true failure on squats anyways. Since it incorporates so many large muscles, there's already almost always another rep if you want it bad enough. Love the pain.
You should increase your working weight by 5 lbs or so each session. By the end of the cycle, unless you start with a decent squat (mid-300's or higher perhaps), you should be using about your old 5-RM.
This is a HYPERTROPHY program, not a strength program as others have noted. While your max will naturally increase a bit, it's more your work capacity and endurance, along with physical mass, that actually increases rather than strength. It would be good to follow this program up with a strength cycle (or, even better, something conjugated so you can retain your mass gains).
Keep in mind that there is absolutely no reason to terminate a set short of losing consciousness. Just breathe, but don't wait around excessively. It's not uncommon for the set to last 4-5 or even more minutes. Hope you have a nice trap cushion on the upper back.
Search around the internet for "breathing squats" or "20-rep breathing squats" or "20-rep squats" and you'll find a few outlines on variations and full programs. There's a good article on BB.com. Or just purchase the book -- it's cheap.