How can you level up quick in wow?

The easiest way if to Recruit a Friend (or RAF). This way you will receive 3x experience therefore leveling up at a faster rate.

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If you do not have recruit-a-friend, then the best way is still to quest, do dungeons, and grind it out. Also, if you happen to already have a high level character, and enough badges/stonekeepers shards, the investing in some BoA (Bind on Account) gear. If you get the chest and shoulders, this will give you 20% extra XP from killing mobs and completing quests. There is also a ring, for another 5%, but that is from the Kalu'ak fishing derby and is harder to get. Joining a guild can be helpful as well as generally guild mates will make gear and weapons, enchant, glyphs and other services for their guild members free or at a severely reduced cost.