1. You need to hit 90. Pick up your legendary quest by visiting Wrathion in the Tavern of the Mists. http://www.wowhead.com/npc=64616

2. You may optionally do Scenarios and Heroic Dungeons, but there's really no particular need. They have been effectively obsoleted, though you can run for Valor Points. You can get a guaranteed 450 weapon from the Arena of Annihilation scenario as soon as you ding, if you're interested.

3. At 90, you will get a quest to go to Timeless Isle, where you will get up to item level 480 in a few hours, and 490 soon after.

4. At item level 480, you may queue for the Throne of Thunder LFR, where you will be automatically grouped with 24 other people for a run through the easiest of the raid difficulties. ToT LFR drops 502s.

You might continue to get gear up to about ilevel 535 (543 with Item Upgrades) from Timeless, and 522 (530 with Item Upgrades) from the vendors who sell based on Kirin Tor Offensive rep earned in Throne of Thunder.

5. At item level 496, you may queue to enter Siege of Orgrimmar LFR, where you will be automatically grouped with 24 other people for a run through the easiest of the raid difficulties. SoO LFR drops 528s.

6. Somewhere between item level 520 and 540, you will get into a Flex run for SoO. A Flex group must be pre-formed, like a real raid, and has raid mechanics similar to Normal. You will probably see people advertising to make Flex groups in Trade chat. Flex drops items of ilevel 540.

7. When you get into the 540-550 ilevel, you will be looking to start Normal raids. At that point, you will probably want to be in a guild that is running them with a regular group. Normals drop items of level 553.