Since Dragon pokémon are weak to only Dragon and Ice moves, you definitely want to bring some Ice pokémon with you. Beartic in particular is a great choice, because its Icicle Crash move, paired with its high Attack stat, is sure to give you some one hit KOs.
However, the tricky part of this gym is that some trainers, as well as the Gym Leader, have Druddigon, which learns Revenge, a Fighting move, at level 35. Because of this, you don't want to bring Ice pokémon up against it, because they are weak to Fighting moves. If you have Archeops, it learns DragonBreath at level 31, which gives it a super-effective move against Druddigon without being weak to any of its moves. If you didn't choose Archeops, though, then you can try using Crustle, whose high Defense stat might make up for its lack of super-effective moves against Dragon pokémon.
Guide to the Gym Puzzle
The puzzle in this gym consists of dragons that you must walk on in order to proceed. Each dragon has a switch on each arm, and pressing the switch will raise or lower that arm. This will cause the dragon's head to move to a different position. You will need to try different combinations of arm settings to get the dragons to point where you need them to point. There are also one-way ramps on some of the dragons.
Guide to the Trainers
First you'll encounter Ace Trainer Webster wo has an L41 Fraxure.
Next is Ace Trainer Olwen with an L41 Deino.
After that is Ace Trainer Jose with two L40 Fraxures.
Then is Ace Trainer Clara with an L41 Fraxure.
Next is Veteran Hugo with an L42 Druddigon.
Next you encounter Ace Trainer Tom who has an L39 Deino, Fraxure, and Druddigon.
After that is Ace Trainer Dara with an L40 Deino and Druddigon.
Finally you encounter Veteran Kim who has an L40 and L41 Fraxure.
Gym Leader Strategy
The leader of this particular gym depends on which version of the game you are playing. In Pokémon Black, you will battle Drayden, and in Pokémon White, you battle Iris. There is hardly any difference between the pokémon that the two have. Drayden has all male pokémon, and Iris has all female. Also, Drayden's Druddigon has the Rough Skin ability, while Iris's has Sheer Force instead.
One of the leader's pokémon is an L41 Fraxure that knows Dragon Tail, Dragon Dance, Assurance, and Dragon Rage.
Another is an L41 Druddigon that knows Night Slash, Revenge, Dragon Tail, and Chip Away.
Finally, there is an L43 Haxorus that knows Dragon Tail, Dragon Dance, Slash, and Assurance.
After the Gym Leader
Once you have defeated the Gym Leader, you obtain the Legend Badge, which ensures that all pokémon of any level will obey you. In addition, you get TM82 Dragon Tail.