How do I open the Gym?

When submitting a question, try to be as descriptive as you can. It helps us to answer your question more accurately.

In this case, I have no clue what gym you are talking about, or what city you are in. Next time try to include this information so you can help us to help you.

Here are two gyms that I think you may be referring to:

Viridian City Gym:
In the beginning of the game, the first gym you will encounter in Viridian city will be locked on purpose. You are supposed to skip this gym, and come back to it last after defeating all of the other gyms.

Cinnabar Island Gym:
The Cinnabar Island Gym is locked for unknown reasons. You are meant to try and find the Secret Key that will unlock it somewhere on the island.
It will be located in the Pokemon mansion right next to the gym. Once you find it, you will be able to use it to enter the gym.

Hope I helped.

That was an excellent answer liz, I commend you (: