BYU on-campus housing has mostly a freshman population-very few upperclassmen live on campus. Be sure to research the dorms and sign up early; the three complexes vary widely, and depending on what you are looking for, one may be preferable over the others. Even if you don't have a preference, early sign-up is recommended since the dorms will fill up completely, usually by early April.
While some of the dorms may be old, they are clean and well-maintained. They are small and don't offer much in the way of amenities. Deseret Towers does require using communal bathrooms. Heritage Halls gives you more of an apartment-like experience. All of the dorms have the same strict rules, and there is no getting around them. The opposite sex is only allowed in your room during visiting hours once a week, and the door must remain open. The lobbies close before midnight each night and are patrolled thereafter. However, this is more a safety measure than a Big Brother-type of thing. The dorms are very safe, so Mom and Dad won't have to worry about you during your first year.