Air
Miami Airport is located in the western part of the city and is one of the busiest airports in the world. It serves a lot of the traffic between North America and Latin America and therefore there is quite a lot of Spanish spoken here. The airport is often very congested and busy so leave plenty of time to spare if you are travelling to or from the airport. There are direct flights here from many European cities and most of the larger cities in the Americas.
There is a free shuttle to the nearby Tri-Rail station as well as to Metrorail and Metromover. You can also take the J or 150 bus to Collins Avenue for a northbound S or 120 bus. This bus also takes you to the Metrorail station at the Earlington Heights.
Fort Lauderdale International Airport is about 25-40 minutes away from Miami. It does have less international traffic but if you do manage to come to Miami through here, it could save you time in the long run as customs, immigration and security move much faster. There is a free shuttle to the Tri-Rail station nearby. This connects to Miami airport, not downtown Miami.
Rail
Amtrak's Silver Service operate two trains each day to Miami from New York, Washington D.C., and other cities along the east coast. The New York to Miami journey time can take as long as 24 hours so be prepared.
The Tri-Rail operator serves Miami from West Palm Beach, Boca Raton and Fort Lauderdale. The frequency of this service during weekdays is once per hour. During the weekend this changes to once every 2 hours.
Within Miami, the Metromover is a very useful way to move around and is free of charge. The Metrorail is a single-line elevated rail system that serves Miami and surrounding environs with 22 stations.
Bus
The Greyhound Bus Company serves Miami. You can travel to or from many American cities directly or through bus transfers.
Within Miami itself, Metro-Dade Transit offer bus connections within the town. Check out what route you need here.
Car
There are three main highways coming into Miami. I-95 stretches along the Atlantic coast of America, terminating in Miami. I-75 comes in from the mid-western U.S.A. and goes through Atlanta and Tampa before finishing in Miami. Florida's Turnpike is a toll road mainly useful if you are driving in from Orlando. U.S. Highway 1 is the only southbound route from Miami and runs through the Florida Keys all the way to Key West.