As soon as you descend into the ruins of N's Castle, you'll run into none other than N himself! He'll say a bunch of stuff and then will ask if he can follow you around, which you should say yes to.
There aren't any wild Pokemon in here, unfortunately, but you can enter the room just to the north of the entrance to find N's old room, which he will talk about if you bring him inside. There's a Luxury Ball over by the train set, but that's about it.
Out in the main hall, you won't be able to head straight east, so climb down into where the water once flowed, picking up the Protein over to the west before heading east.
In the eastern-most part of the room, down one of those little ledge things, you can find TM50 (Overheat), a powerful Special-base Fire-type attack that lowers the user's Special Attack by two stages afterwards.
Climb up the stairs and follow the path forward until N stops you, saying you should go forward alone. Keep going and you'll enter the room where the you fought Reshiram/Zekrom, N, and Ghetsis in the original Black and White, except it's in shambles.
Head forward and N will follow after you. After some talking, he'll release his Zekrom (Black 2) or Reshiram (White 2) and will then ask if you want to battle. If you're ready to take him on, say Yes, otherwise say No and you'll be given a chance to heal and save.
N uses Zekrom if you're playing Pokemon Black 2 or Reshiram if you're playing Pokemon White 2. He does NOT use both on his team.
Even though he uses only one Pokemon, it's an uber legendary Pokemon and is very strong, meaning you will be in for one heck of a fight, especially if you haven't done much training after beating the game.
Catching a Pokemon like Excadrill can help a lot against Zekrom, because it is immune to its powerful Fusion Bolt attack while resists its other attacks, Zen Headbutt and Dragon Claw. You may have to train it up a bit, though.
If you're playing Pokemon White 2, catching a high-level Pupitar on Route 15 (east of Nimbasa City and across the bridge) and then evolving it into Tyranitar is an effective strategy. Tyranitar resists Fusion Flare, is immune to Extrasensory, and gains a Special Defense boost from the Sandstorm it whips up thanks to it being a Rock-type, meaning it will reduce the power of Reshiram's Dragon Pulse.
Regardless of which one you have to fight, getting TM26 (Earthquake) on Route 15 is very helpful, as is any Dragon-type attacks you may have. Be careful about using your own Dragon-type Pokemon, because his are both fairly quick and their high level doesn't make it a walk in the park.
After beating N in his castle, you'll be able to run into him in the Ferris Wheel on Fridays in Nimbasa City. Once you've ridden with him on the Ferris Wheel, he'll return to his castle, where you'll be able to battle him.
He uses a different team depending on which season it is, with levels ranging from level 75 to 77, making him very tough to take down. You can only fight him once per season.
After beating him, he'll talk for awhile and eventually return the legendary Pokemon to its stone. This means he'll return Zekrom to the Dark Stone in Black 2 and Reshiram to the Light Stone in White 2. He'll give you that stone afterwards, which you then need to bring back to the Dragonspiral Tower north of Icirrus City.
This means you should return back to Opelucid City, head west onto Route 9, and then enter the Tubeline Bridge, which is finally open.
Meet your Meteor!
While you're visiting Opelucid City, you can return to Drayden's house in the middle of town with just about any Dragon-type Pokemon to have him teach it the powerful Dragon-type Draco Meteor attack. He will teach it for free and as many times as you like, so feel free to reward your dragons with a powerful attack! Just keep in mind that it lowers the user's Special Attack by two stages afterwards, but it can be a nice attack on Dragon-type Pokemon with high Attack so they can keep attacking afterwards.