Summarize:

You cannot start the quest to reach Pandaria until level 85. If you're desperate to get there earlier, you can ask a warlock or mage for a portal at any level. Once you are level 85 and own the Mists of Pandaria expansion, you'll get the King's Command quest as soon as you enter Stormwind. If your quest log is full, remove a quest and talk to Varian Wrynn in Stormwind Keep or check one of the Hero's Call Boards in the city. A bug may prevent players who purchased a level 90 boost from getting this quest. You should be able to jump straight to The Mission quest, described below. A cinematic will begin as soon as you approach the castle proper in the center of the keep. Watch King Varian and the admiralty talk about a shipwreck on an uncharted island. After the cutscene, your character will be standing in front of Rell Nightwind. Speak with Rell to accept the next quest: The Mission. The massive flying gunship called the Stormfire hovers in the air north of the docks. Fly up to the gunship on a flying mount, or ask someone with a two-person mount for a ride. Another cutscene will start, and you will begin the journey to Pandaria.
Reach level 85. Enter Stormwind to start the quest. Enter Stormwind Keep. Talk to Rell Nightwind to accept The Mission. Fly to the gunship north of the Stormwind harbor. Talk to Sky Admiral Rogers.