First and foremost, the best way to level up the fastest is actually through questing, where you actually go on specific missions for various characters and pick up items, kill enemies and creatures, deliver messages, escort comrades, and so much more. WoW powerleveling is something that is pretty fundamental and the best way to get started is simply through playing the game itself.
The best way to get a lot of quests done in the fastest way possible to power level the quickest is to actually pick up as many quests as you can in one town or map area, and then go out and complete them. This way you can accomplish multiple quests while you are out and then return to turn them all in at once and receive all of your experience points and rewards in bulk. This is the way that most professional gamers actually play, they simply take the time to get through the game efficiently and map out their moves before they head out to complete quests and level up.
Now, grinding to level is one tactic that a lot of gamers tend to live by. The strategy requires you to really "grind" away by attacking mobs of creatures and enemies through the world of warcraft and gaining experience points through all of your kills and item pick ups from slain enemies. This can be a bit tedious but is a good strategy to level quickly if your character is of warrior class and you can speed grind your way through maps, but its always a good idea to get quests done as well. You can actually grind your way through quests and actually get the best of both worlds to level very efficiently.
You should simply get your quests and as you move around the map areas grind away on the enemies and creatures in the area so that you build experience points as you move about the area completing your quests as well. Certain quests will require that you slay multiple enemies as it is so you can hone your combat skills and level pretty quickly as you move around completing quests. These are just some very simple strategies to get the most out of questing and grinding at the same time to level through the world of warcraft power guide efficiently.