My thoughts:
-Get into a guild that is lv 6 (or 7, i think it is 6). This means you will get an EXP+ Bonus on kills.
-If you are starting fresh, pick up 1 Gathering professions (however 2 is always great). Use these to make money (via selling goods on the AH).
-Either pick a Healing or a Tanking class, and then be a Healer or a Tank. Upon hitting lv15 you can start using the Random Dungeon tool. This puts you into a dungeon make up of people across many realms. DPS are everywhere, being a "needed" role means later on you can be more helpful to your guild/get into a better one. But the best of being tank/healer is the Wait time for said dungeons..it is almost instant.
Some say Questing for levels is faster then running dungeons. However, I did 1-80 on a Prot Warrior with 7 /played days. He had under 250 quests done.
However I did have Account Bound gear to help me, but you an 100% gear up in dungeons.
The only down side is you are going to run the same places many many many times. By the time you really start to hate that dungeon, you move onto the new few.