You have to apply to become a citizen; it is not automatic. Marrying a U.S citizen only makes you eligible to apply. The application is a legal petition that requires compelling evidence, forms, and filing fees.
Even if your application is granted you do not become a citizen, you become a permanent resident/ green card holder. Legal Permanent Residents (LPRs) do not have the same rights that a U.S. citizen would have. LPRs are not allowed to vote. They have to spend the majority of their time within the United States or they risk losing their immigration status. LPRs are subject to deportation at all times, so getting arrested or being convicted of a crime comes with an extra level of consequences.
Permanent Residents can apply for their immediate family members to also become permanent residents. But unlike the process for immediate family members of citizens, the process for immediate family members of LPRs may have extensive waiting periods depending on the country where their relatives live.
Three years after receiving your green card through marriage, you can apply for full citizenship. (Other types of green cards require a five year waiting period before you can apply for citizenship.)