Miami International Airport is the hub connecting the southern hemisphere to North America, so naturally it’s big and busy. It’s less than 20 minutes from Miami Beach if there’s no traffic, but given the crowds at MIA, the Fort Lauderdale Airport (only 20-30 minutes further) might sometimes be the better bet. Both are served by shuttles and cabs are plentiful, but one advantage MIA will have beginning in 2012 is a stop on the Metrorail system.
Miami might be a car-bound culture, but the public transit system is actually quite usable in some places. The Metrorail transit system runs the length of the city and a fun free monorail system moves people around 21 downtown stations. Though bus service is not frequent in most areas, with more than 100 routes, it should get you to the Metrorail in a pinch.