Travel - How to get from city to city

Around level 5, you will head to your second zone, a small town outside your faction's home city.  In this town you will get a quest to buy a ride to the city and make a delivery there.  The gold ? you see when accepting that quest will by the flight master.  You always want to know where the flight master is, so go to your minimap in the upper right hand corner and click on the magnifying glass.  You have an option to click the flight master so one will always show up if near.  (You should also click some other things if you haven't done so, things you will need to find as you level.  I talk about that elsewhere.)  Check the flight master so that even if you don't do that quest immediately, he will always be easy to find when you are ready. 

Alliance ride on giant eagle-like gryphons

Horde fly around on giant bats

You also have ways to travel from continent to continent.  There are boats, zeppelins, and portals.  That's for later.