I see I'm late here. But if it helps other people, here's a go.
Taiji breathing depends on the kind of movement you do and is grounded in the yin-yang theory (not just duality but ever-changing duality).
There are 4 phases to breathing - inhalation, pause, exhalation, pause. And there are 4 primary physical jing or energies: peng (wardoff), ji (press), liu (rollback) and an (push) (you may want to read up on this, it's too much to explain here). Every taiji movement is an interplay of the 4 energies and each of them is linked to a particular kind of breathing: inwards or outwards, rising or sinking. You can see this the most clearly in fajing movements where breath follows the body for the best 'force'. It's worth noting that nothing is rigidly tied, a master may well do something internally and something else externally.
Also, the classics identify two kinds of breath - 'soldier breath', where fast movement naturally demands upper-chest rapid breathing trying to pull in maximum oxygen (think of running or jogging); and 'scholar breath', where slow, deep breathing starting from the diaphragm and utilizing as much capacity of your lungs as it can, brings calmness (think meditating). Taiji has both of these - some slow movements, some fast, some explosive, some gentle. Also a particular movement can be done fast-style; it can be done slow-style depending on your intent - are you practising that morning as a peaceful start to your day or are you all energized and want a martial art start?
Usually beginners are asked not to worry about breathing and just concentrate on their movements since concentrating on breathing at this point is asking for the cart before the horse - it takes focus off aspects that need to be polished first like posture and technique and makes the movements jerky. The only thing you should remember to do in the beginning is just breathe normally (you'll be surprised how many times people are caught holding their breath). Once you are grounded in the principles of the art, the breathing becomes automatic and you don't have to think about it consciously.
Lastly, find a teacher you respect - a good one is more precious than gold or diamond, like a second father/mother, irreplaceable. Mine taught me this and I pass it on.