[Pernicious]

Well, when you first enter, make sure you go through the Dark Portal and not get summoned in. When you do that, you'll find a quest just down the steps and to the left for Alliance, right for Horde. That will put you on the right path. You'll be taken to the first town of your faction and be presented with several quests to begin your adventures in the Outland. Leveling from 60-70 will take a lot longer than it took you to level up to 60, so enjoy it as you progress. I currently am going through the process for the third time (first time as a Horde) and have settled on this order.

Hellfire Peninsula, Zangarmarsh, Terokkar Forest, Nagrand, Blades Edge, then Netherstorm/Shadow Moon Valley. I typically like to play a zone until completion and all the quests are gone before progressing to the next. I suggest the same so that you can experience everything. You'll want to save money as you go since level 70 becomes very expensive between spells, professions, and mounts.

Good luck!