After you defeat Brycen, you find Cheren and Bianca outside of the Gym. They talk a little bit about how much they have grown and changed, and how they're still figuring out their goals as trainers. But then Brycen steps out and can sense the Shadow Triad. They tell you that Ghetsis and N are waiting at Dragonspiral Tower. Brycen and Cheren will head in the direction of Dragonspiral Tower, which is north of Icirrus Gym.
Some new pokémon that you can catch outside of Dragonspiral Tower are Mienfoo and Druddigon. Druddigon can't be found outside of the tower during Winter, but can be found inside of the tower at any time of year. You will also find Golett inside of the tower.
A few pokémon that I recommend bringing are Ducklett, Litwick, Frillish and Ferroseed. I also strongly recommend catching a Golett before you head up to the fourth floor, because it will come in handy against the Team Plasma grunts.
Also, if you want to, you can bring a pokémon that knows Strength, because there is a boulder on 2F that can be pushed with it. However, you don't need to push that boulder to get to the top of the tower.
When you approach the entrance to the Dragonspiral Tower area, you find Professor Juniper's dad, Cedric, outside. As you go up to him, Bianca will arrive. Cedric will tell you that a large group of Team Plasma grunts has taken over the Tower. He mentions the legend of the dragon atop the tower. Bianca asks to stay back with him and be his bodyguard. Cedric will give you an Old Gateau.
When you go into the Dragonspiral Tower area, you find a Team Plasma grunt standing outside, just south of the bridge leading up to the tower. This grunt doesn't fight you. The bridge to the north is surrounded by water, and some of the pillars are broken and gone. In fact, you can Surf from the east side of the bridge to find another area where there are a couple of Ace Trainers.
Ace Trainer Jesse has an L36 Vanillish and Galvantula. For Vanillish, use Klink or Litwick. For Galvantula, use Litwick and attack with Fire, or use Excadrill and attack with Rock moves.
Ace Trainer Jamie has an L35 Cubchoo, Darmanitan, and Leavanny. For the Cubchoo, try using Ferroseed and attack with Steel or Rock physical attacks. For Darmanitan, Frillish is a great choice for an opponent. For Leavanny, use Litwick.
You can get TM63 Embargo here. Surf around with your Dowsing Machine on to find a Heart Scale.
Now you can go on into the tower. There are no trainers on the first floor, although there are wild pokémon. When you approach the stairs to 2F, you'll hear a commotion from the top of the tower.
On the second floor, you will find Cheren, who will tell you to walk on the fallen columns. Then he'll continue up the tower. Go up, push the Strength boulder if you wish, then go up under a column, and to the right and down to get the Hyper Potion. Then climb up onto the fallen column that is to the right of where the Hyper Potion was (the cracked part of the column is like a slope). Follow the columns until you get to the ledge where Cheren was. Get the Stardust from on top of the column. Then go up to the third floor.
On the third floor, there are some ramps that you can jump from to get to the various parts of the room. Start by hopping down the first ramp that you can reach from the stairs. Then, to get the Shiny Stone that you see at the upper-right part of the room, use the middle ramp and then just follow the rest of the ramps that you encounter and you'll get to the Shiny Stone. Finally, use the bottom-most ramp to get to the stairs to the next floor.
You will find that Brycen and Cheren are holding off the Team Plasma Grunts so that you can get upstairs. However, you will have to fight a few grunts of your own to get to the top.
The first grunt has an L34 Watchog. Use Litwick against it.
The next grunt has an L34 Liepard. Use Ferroseed, Scraggy, or Klink against it.
After that, there is a grunt who has an L34 Scraggy. Use Ducklett against it and attack with Flying moves.
Next is a grunt who has two L33 Liepards. Use Ferroseed, Scraggy, or Klink.
Finally, there is a grunt who has an L32 Watchog, Krokorok, and Scraggy. Use Litwick against the Watchog, and Ducklett against the Krokorok and Scraggy.
After fighting the last grunt, go to the right to get a Dragon Fang.
The third floor has a floor made of concentric rings. You will have to take the correct path to get to the items and exit.
From the entrance to 5F, start by going to the right. Cross the small stone bridge, then head left and cross another stone bridge to get a Star Piece.
Go back down the bridge, then head right, then go down the two bridges and head left to get a Stardust.
Go back and up those two bridges, then head left and go up the bridge to the inner ring of the room. Go to the right and over the ramp, then down the bridge. Head left, down another bridge, then go all the way to the right to get a Revive.
Finally, go left and down a bridge, then left again and up the stairs to the sixth floor.
Here you will find Giallo, who is one of the Seven Sages, along with four Team Plasma grunts. The grunts will surround you, forcing you to battle all four of them with no breaks.
First you encounter a grunt who has an L33 Watchog and Krokorok. Use Litwick against the Watchog and Ducklett against the Krokorok.
The next grunt has an L34 Krokorok. Use Ducklett against it.
Next is a grunt who has an L33 Trubbish and Liepard. Use Golett against Trubbish, and Ferroseed, Scraggy, or Klink against Liepard.
Finally, there is a grunt who has an L34 Watchog. Use Litwick against it.
At the top of the tower, you find N, who has awakened one of the legendary Dragon pokémon. If you are playing pokémon Black, it will be Zekrom. If you are playing White, it will be Reshiram.
N will tell you to find the other Stone to revive the other Dragon pokémon and fight against him. If you are playing Black, he tells you to find the Light Stone. If you are playing White, he tells you to find the Dark Stone. He departs with his legendary pokémon to go to the Pokémon League and defeat the Champion.
Once N flies off, Brycen and Cheren will arrive and the three of you will go back outside, where you will meet up with Bianca and Cedric. Alder will also show up and urge you to find the other legendary pokémon and fight N. Alder says that he suspects that Relic Castle is where you can find the stone to revive the legendary Dragon. That's your next destination!
Don't remember where it is? You can reach it from Route 4, which connects to Nimbasa City to the north and Castelia City to the south. So, warp to one of those cities, get onto Route 4, and head west on the road under the freeway to reach Desert Resort. In there, walk along the eastern wall, then head toward the statues when you see them.