After you reach Opelucid City, you can challenge the Opelucid Gym.
Go through the Gym
Near the entrance, Clyde will give you a Fresh Water and give you some advice: use Ice and Dragon moves against Dragon-type pokémon.
I recommend having Skarmory on your team for this gym, because it is resistant to many of the moves that you will encounter here.
Follow the lighted path, then go north on the dragon until you reach Veteran Lucius. He has a level 46 Fraxure. I recommend using Magneton/Magnemite/Magnezone, Lucario, or Probopass on the Fraxures that you will encounter in this gym.
Go back to the dragon's head and step on the middle of the plus-shaped platform. An arrow will light up. Step on it. After the dragon head rises, other arrows light up. You can step on them to make the dragon move.
If you step on the left arrow, you meet Veteran Rhona, who focuses on defense. She has a level 45 Fraxure and a level 45 Druddigon. Skarmory is a good opponent for Druddigon. However, the Druddigon has Rough Skin as well as a Rocky Helmet, which causes your pokémon to get hurt when you attack it. Also, it uses Protect and Substitute, making it difficult to land an attack. It also uses Swagger, which causes confusion.
Now go back to the dragon head and step on the right arrow, then when the dragon stops moving, step on the right arrow again. You meet Veteran Jerry, who focuses on attack. He also has a level 45 Fraxure and a level 45 Druddigon. Jerry's Druddigon knows Flamethrower, so I recommend having Aron/Lairon/Aggron or Probopass, or Keldeo if you have it. If not, bring Scraggy/Scrafty.
You only have to defeat one of these veterans to make the up arrow appear on the dragon's head. Feel free to skip a veteran if you want, but you might want the experience.
After going farther up, step on the left arrow to go to Veteran Denae, who will challenge you to a rotation battle with a level 44 Fraxure, a level 44 Druddigon, and a level 44 Axew (use Magnemite/Magneton/Magnezone on Axew).
If you go to the right, Veteran Ron will challenge you to a triple battle with a level 44 Fraxure, level 44 Druddigon, and level 44 Axew (use Magnemite/Magneton/Magnezone on Axew).
You only have to defeat one of them to go up to Drayden.
Drayden has a level 46 Druddigon, a level 46 Flygon, and a level 48 Haxorus. Against his Druddigon, I recommend using Skarmory or Genesect (if you have it). Against his Flygon, I recommend using Skarmory. Against his Haxorus, I recommend using Cobalion if you have it, or otherwise, Lucario, Probopass, Pawniard, or Aron/Lairon/Aggron.
After you defeat Drayden, you receive the Legend Badge, which allows you to control traded pokémon of level 80 or lower. Drayden also gives you TM82 Dragon Tail. Then Drayden asks you to wait outside so he can come down and tell you about the legendary Dragon that created Unova. Go down to the dragon's head and use the down arrows until you are at the lower level. Go south to exit the gym.