Trumpeter James Morrison has a wonderful YouTube video series where he addresses the essential fundamentals of playing the trumpet (or any brass instrument for that matter). His way of explaining breathing, endurance, range and more is simple, clear and highly-effective.
A few key concepts to keep in mind:
- A relaxed deep inhale produces a focused exhale
- Slow air equals lower notes; Fast air equals higher notes
- Air powers the horn, not the lips
- Use less pressure (mouthpiece on lips) to play higher; relax your dominant arm holding the horn to your face
- Completely envision every detail of your sound before you play