Breathing ladders were a new concept to me. I'm not sure where I first heard of the concept, but then I saw it everywhere. Essentially, what you are doing is taking and exercise and pairing it with controlled breathing, working up in reps, and then down in reps.
Each rep corresponds with one breath. Two reps, two breaths, 18 reps, 18 breaths. Get the picture?
The concept is to try to force the diaphragm to breath efficiently and to cut out the habit of mouth breathing. Controlled stress. It's also a very easy way to get in volume. A ladder from 1 rep to 20, back down to 1 rep, would yield 400 reps.
The breath should be in through the nose and work to feel the lateral ribs expanding. Work the diaphragm. It often helps to breath out the nose as well. Just keep the mouth shut.
An example for a nice exercise would be a kettlebell swing. One swing, put the weight down, one big breath. 2 swings, put the weight down, 2 breaths.
Play with this style of exercise and training and see if your breath, recovery improve as you get in quality volume.