A few years ago I started to run, for the 2st few week I was depressed at how quickly I was out of breath. I stuck with it and things started to turn around quickly after that. I never specifically targeted my breathing. I did at times try breathing differently, but I just kept running and shit got a lot easier. While I'm sure there are breathing techniques you can practice that can help you progress faster, just keep exercising and you'll get better regardless.
And not to discourage you, but at least for me after I got less winded and could run farther I then had to deal with shin splints. I will say my honest opinion's that the initial phase of getting into shape sucks. But the bad shit passes and before I knew it I was able to run 3 miles without stopping. That was my goal so I never pushed any farther than that. It's pretty remarkable how the human body adjusts and grows from exercise.
For reference I'm 5'11 and was about 240lbs when I started jogging. And as far as physical activity level prior to that, there was non. What helped me the most was my music to be honest, I have the Nike+ and my iPod and when I was ready to start walking I'd press the power song button and get a boost to keep me going.