According to yoga teachings, exhalation (breathing out) is the key to ideal breathing. You are also encouraged to breathe slower and longer, but ensuring that the lungs are emptied effectively is the key.
What Is Ideal Breathing? How Do You Do It?
It is when you breath slow and deep and through your noes
You should breathe from your stomach and not your upper lungs (at first push out your stomach while breathing in, you'll get the feel for it after a bit of practice). Also ideally you should only breath about 6-12 times a minute (compared to the average 45), in deep slow breaths.
Along with the previous answers, it is also said that inhaling through your nose helps, as nose hairs and such 'filter' the air of impurities.
Suck in air trough your nose, preferably, but you can do it through your mouth, and the blow it out through the same place you started.