Two answers to this, depending on your spec and your skill level:

Answer One:
The first is to spend a few thousand gold to buy all the crafted PVP gear for your class and run Hour of Twilight heroics and Raid Finder until you can replace most of it. I don't want to start a debate on the ethics of using PVP gear in PVE, but if you're a DPS class and can still put out decent numbers, this is a reasonable way to get going. DO NOT do this if you are a tank or healer... it won't end well.

Answer Two:
I'll pretend you *just* hit 85 and have crappy quest gear. Your goal is to hit ilvl 353 as fast as you can so you can get into the new Hour of Twilight heroics.

- Buy cheap ilvl 378 BoEs on the AH
- Buy crafted ilvl 359 armor and ilvl 365 weapons (these can be expensive)
- Do enough questing in Hyjal to unlock the Molten Front dailies; one day of those dailies will open a vendor who should have at least one ilvl 365 item you can use
- Go to Hyjal and complete the Thrall questline for a 365 cloak

This will probably get your ilvl in the 330s. Here you have a few options:
1. Queue the 85 normals to farm JP
2. Queue the regular Cata heroics to farm JP and VP
3. Farm BGs for honor to convert to JP

Option 1 is super easy, but slow and boring. I don't recommend option 2 because most of the people in those dungeons are also too low on gear for the new heroics, so the failure rate is high enough again to make the return per time invested very low. If you go with option 3, you might want to pick up the crafted PVP set for your sanity's sake.

Once you reach 353 ilvl, run the Hour of Twilight heroics for JP, VP and 378 drops.

Once you reach ilvl 372, you can run Raid Finder for more stuff, and you're also geared enough to not be a huge burden in normal mode DS.