Just to flesh out robyng's excellent responses - the TRI-RAIL is a rail line that travels between Miami-Dade, Broward and Palm Beach Counties (hence the "Tri" in the name). It is primarily intended for commuters, but is also used by some leisure travellers. Although Tri-Rail goes nowhere near Downtown Miami (let alone the southern portion of Miami Beach, where the nightlife is), it comes into play because a traveller at MIA would take Tri-Rail a couple of stops to the "inter-modal" transfer station where Tri-Rail junctions with the METRORAIL.

Metrorail, a more traditional urban rail (all-elevated, no underground) system, essentially runs between Hialeah, Downtown Miami, the University of Miami area of Coral Gables and its terminus at the Dadeland shopping/commerce district. At a couple of the Downtown stations, Metrorail connects to the People Mover, which is handy for getting around the various subsections of the greater Downtown area. There is only one Metrorail line, and service is spotty at the best of times. In the section between Hialeah and DT, it slao travels through some fairly dicey neighborhoods (it is not called the "Metrofail" for nothing).

As robyng stated, there is a Miami Beach-bound bus that picks up at one of the downtown Metrorail stations, but this service is very limited and geared toward daytime service (serving people going to and from work).