U.S. Citizenship can either happen automatically if born on U.S. soil or incorporated territories, or if born overseas of two or one U.S. parent. Strict requirements apply in the latter case and vary according to the year of birth of the applicant. Thus, it is always recommended to speak to an experienced immigration attorney about your specific situation.
Alternatively, one can become a citizen via an application for naturalization, usually after having held a green card for a certain number of years. There are also minimum requirements to meet such as of good moral character, continuous presence and physical presence in the United States.