The Driftveil Gym focuses on Ground-type pokémon. Bring water, grass, and ice pokémon with you.
In Driftveil Gym, you have to reach Clay by using elevators. Go up from the entrance and get on the elevator up above. Check on the blue thing on the top right to make it go down.
Go up and talk to Clyde to get your free Fresh Water. He'll tell you that the platforms that you have been to will light up and will help you figure out where to go. Go north to reach the main part of the gym.
Go north from the first platform to encounter worker Noel, who has a level 31 Baltoy.
Go east from him, then south (check on the yellow sign if you want to see more of the platforms), then east. You'll reach worker Tavarius, who has a level 29 drillbur, a level 29 baltoy, and a level 29 sandile.
There are other trainers here, but they are optional.
Go north from Tavarius, then north two more times. Go east, then south, then east, then north to reach Clay.
Clay has a level 31 Krokorok, a level 31 Sandslash, and a level 33 Excadrill.
When you defeat him, you get the Quake Badge and TM78 Bulldoze.