1) Breathe through your mouth – You just can’t get enough air through your nose quickly enough.  Plus, in through the mouth sets up a reflex that is logically followed by exhalation through your mouth.

2) Breathe in time right before you play – At an early age, students should be taught to breathe in time right before they play.  Mark in breaths to breathe in time between phrases.

3) Your air has only two speeds, IN and OUT – Be careful not to stop the air between inhalation and exhalation.  It should feel a lot like a wind up and a pitch, throwing a ball with in one motion.  Stopping in the middle will often cause tension or obstruction.

4) Keep center of your lips on mouthpiece when breathing in – Dropping your jaw for a “big breath” or otherwise needlessly removing the mouthpiece from contact with your lips will delay the release of your air.  Even more importantly, if you don’t keep your lips close they will not be prepared to vibrate.  

5) Breathe in through corners of mouth – This goes along with the previous piece of advice.  I tell my student to imagine their lips are in the shape of a sideways figure eight or infinity symbol: ∞.  Lips are touching in the middle and corners relax to bring in air.  Notice this breath as a great example:

6) Breathe in across your tongue – Practice this by breathing in while raising/moving forward the front half of your tongue enough to feel cold air rushing against past.  This provides something for the lungs to draw air against and sets up your tongue for an effective playing position in most registers.  It also prepares tongue to release the air immediately.  Without this, you may inadvertently close your throat, constricting the flow of air and creating a point of tension that is not helpful for playing.  Notice in this video how the player’s tongue comes forward for a good breath and to prepare for the subsequent articulation: