Cold Storage is south of Driftveil City.
Outside of Cold Storage
There are some trainers around the area, and there is a gap in the fence on the left side where you can get into the area of Cold Storage.
After fighting several trainers, you will reach a building with a door. Cheren will arrive and say that you need to go into Cold Storage to look for Team Plasma, so go inside.
Inside of Cold Storage
There are Workers in this area who have pokémon that you must battle. There are areas of the floor where you will slide around on the ice, so it might take a few tries to get to where you are trying to go.
When you make your way to the end of Cold Storage, you will find an open container. Cheren will arrive and ask if there is anyone in there. It doesn't matter what you answer, but the truth is that yes, someone is in there. Who? Team Plasma, of course! Go on into the container.
A bunch of Team Plasma grunts are in there, surrounding Zinzolin, who is one of the Seven Sages. Cheren will take care of the grunts on the left, so you need talk to each of the grunts on the right and defeat all four in order to progress. One has a Watchog and Sandile, one has a Watchog and Scraggy, one has a Liepard, and one has a Trubbish.
Opening the Gym
Once they are defeated, Clay and his associates will arrive and take Team Plasma away. Now you can exit Cold Storage and head to the Gym.
When you get to the Gym, Ghetsis will be talking to Clay, asking him to return Zinzolin and the Team Plasma grunts to him. Clay grudgingly agrees to let them go with out a fight. After that, the Gym is open for you to challenge.