There's some excellent, 100% advice in this thread. I know I've made every conceivable mistake known to man, and invented a few, learning to run theses calls.
It's so hard to put into words all of the nuances that go into running the trumpet. Hand position is everything, but it must be matched with the right lip pressure, placement and air draw. Do those last 3 perfect, with no hand placement, and you get nothing. Perfect hand placement with an improper lip placement is no good either.. Etc, etc.
As to the original question of air. It took me forever to realize I was trying to draw WAY too much air. The tip of going as "soft" as you can really helps to train your brain. When it's right, you really can run the trumpet for minutes on end, while still breathing through your nose.
When I've got the lip stop position right where I like it (1/16" can make a difference), I'll use my hands and the cup I make with them to adjust tone. Air speed and pressure will aid in volume.
When learning, I would tell someone to constantly experiment with changing the hands, lip placement, and air pressure. When you find the right recipe - just be able to replicate it. That's where the practice comes in.