Hi Arkayeis,
Breathing play an important part of running. Yes, organised breathing method is a proper way of breathing. This is what I do in my alternate day 10Km run. I started my rhythmic breath of 4 steps inhale follow by 10 steps exhale for 1st Km, then 8 steps for 2nd Km, 6 for 3rd Km, 4 for next 5 km and last 2km is 2 steps. You can practice the swimming style of inhalation, practice till you get your own rhythm, in this way you wont run out of breath. Also begin slow and relax look at the horizon and the surrounding.
To strength your lung. follow this link :
Good luck