As always, the white-haired guy at the beginning of the gym will give you a Fresh Water.
The trainers in this gym specialize in Electric Pokemon. Ground Pokemon like Sandile are not affected by Electric attacks at all so they are a good choice to use. This gym is a set of roller coasters. Take the first coaster with the blue track and take the first exit. You'll find a Lady before the switch.
Enter the coaster and ride it to the first exit. Walk north to battle Elesa. She has two Pokemon that are part Flying-type and her Blitzle knows Flame Charge so Grass Pokemon will have a rough time. The easiest Pokemon to use against Elesa at this stage of the game is Sandile because he has complete resistance to Electric attacks.
She will give you the Bolt Badge after defeat. It lets you use Strength outside of battle to moves big boulders. She also gives you TM 72 Volt Switch. It is a special attack that lets the user switch with another Pokemon in your party after the attack hits.
Head to Route 16 at the northeast corner of the city.
Items in Nimbasa City Gym:
Received from the white-haired man at the front of the gym.