First, you need to have a level 90 character. If you don't have one yet, it's okay: the experience required to level from 1-85 was significantly reduced when Mists of Pandaria was released, so you'll be able to catch up quickly. Once you reach 85, hop over to Pandaria and enjoy the new quests. You'll gain a level for each zone you clear, more or less. You can also run some normal mode 5-man dungeons if you'd like, though go easy; you'll be running the heroic versions quite frequently at 90.
Second, you'll want a DPS spec and a good set of starter gear for it. Completing the Dread Wastes or Townlong Steppes quests will get you outfitted; if you don't have DPS gear laying around to actually complete the quests, Len of Arms will happily sell you a set of 408's to get going. You can also search the auction house; many blue BoE's in the ilvl 430-450 range are listed frequently, for pretty reasonable prices.
Filed under: Mists of Pandaria