The first thing I do is dismantle and clean it. This will help you to get to know how your brush works...and just spray water or cleaner first to make sure it is working the way it should.
If you do not do that, make sure the needle is all the way forward as some airbrushes are shipped with the needle back to stop damage from packing and shipping....
Just agreeing with what's been said already. Breaking it down and cleaning it is good, since you will need to when you clean after painting anyway. Also, there have been cases where you get a new brush with a bent needle tip or whatever. Doing a visual check and functionality test is a good idea just for piece of mind. If you know the hardware is in good shape, then it's easier to diagnose any issues you run into once you start painting.