Six of the Team Plasma Sages will talk to you. Before they have a chance to battle you, some of the gym leaders show up and hold them off. Walk northwest through the two pillars. Go east and up the stairs.
Continue east until one of the Shadow Triad appear. He shows you the room where you can heal your Pokemon. Do so by talking to the purple-haired woman. There is a Max Potion in the room east of the healing room. When you're ready, use the eastern stairs to go up to the next floor.
The first room on this floor has a PC to withdraw and deposit Pokemon and items. The next room west has a Max Revive. The western-most room on this floor has a Team Plasma Grunt in the back that will transport you to the Pokemon League. This is very useful if you want to buy more Ultra Balls and Potions or to level up your Pokemon before the upcoming battle with N. The female Plasma Grunt west of him will give you an Ultra Ball. As you approach the western stairs of this floor leading up, a member of the Shadow Triad will appear. Walk up the stairs.
Another member of the Shadow Triad will point out the room to the north. He says it was the world N was provided with. Inside are a lot of children's toys like a train set and a basketball. There is a Rare Candy in the middle of the half pipe. The next room east has a Full Restore. Walk up the eastern stairs to the next floor.
This floor has a large doorway leading to N. As you try to enter the doorway, Ghetsis barges in and reveals his whole plan. He wants everyone to release their Pokemon so Team Plasma are the only people who have Pokemon. Then he will be able to rule the world.
Walk north until N starts speaking. Walk north again once he is done talking. He will meet you in the middle and notice that the second legendary Dragon Pokemon isn't responding to you. He challenges you to a battle and his Zekrom/Reshiram crashes into the room. Your Light Stone or Dark Stone will activate and Reshiram/Zekrom will appear. You have a chance to save before battling Reshiram/Zekrom. Once you're ready, interact with it to initiate the battle.
If you are impatient, using your Master Ball is the easiest way to catch the legendary Pokemon. It isn't that hard to catch, though, so you probably shouldn't waste it. Capturing it is the same as any other Pokemon, just a little more difficult because it can do a lot of damage. Get its health as low as possible and give it a status effect before throwing Ultra Balls at it until it's caught. After catching it, you are given the opportunity to switch Reshiram/Zekrom into your party. N heals your Pokemon and starts a battle.
After the battle, N realizes that people must accept the ideas of others. Ghetsis appears and talks down to N. Cheren and Alder show up and Ghetsis reveals the real plan to them as well. Ghetsis challenges you to a battle in an attempt to eliminate you.
Alder explains to N that even though they didn't agree earlier, that doesn't mean they can't work together. Alder and Cheren take Ghetsis away and N reveals more about his personal story. It turns out that he was beginning to doubt his beliefs after he met you in Accumula Town and noticed your Pokemon actually liked you. The further you were in your journey, the more Pokemon N met that loved their trainers. He tells you to follow your dreams before bidding farewell.
Congratulations, you've completed the main story of Pokemon Black or White. After the credits roll, you see N fly off on his legendary Dragon Pokemon.