In order to accompany the F-1 student, the dependent must obtain an F-2 Form I-20, and either apply for an F-2 visa at a U.S. Embassy or Consulate, or, if in the U.S. in another status, submit an application for a change of status to the USCIS.
Documentation of the legal relationship between spouses* (i.e. official marriage certificate) or parent and child (i.e. official birth certificate or legal adoption papers) must be presented during the visa application process or included in the change of status application. *In order for same-sex spouses to be eligible for F-2 status, the marriage must be recognized in the place of celebration.
Other family members who do not meet the eligibility requirements for F-2 status, but wish to accompany the F-1 student may wish to explore possible alternative immigration options at the U.S. Department of State website.