Mostly, don't overthink it — your body sorts this out better than any rule does. Breathe through your mouth (you need more air than your nose alone can supply), and aim for slow, deep breaths from your belly rather than shallow ones from the top of your chest.
If you're breathing hard and ragged on an easy run, that's not a breathing problem — it's a pace problem. Slow down and the breathing settles itself.
You'll see advice about rhythmic breathing patterns (breathing in for three steps, out for two, and so on). Some experienced runners like it. As a beginner you really don't need it. Run easy enough to breathe comfortably, and let it become natural.