There are frequent flights to Rio from all major cities in South America and from a number of major airports in the USA and Europe. Other gateway airports in Brazil include São Paulo, Recife, Natal - popular with Northern European package tourists - Fortaleza, Belém and Manaus. Brazilian airlines Varig, TAM, and Gol fly to many major cities in the world. There is a departure tax for international flights, but this is often included in the ticket cost.
Brazil has land borders with every other country in South America, with the exception of Ecuador and Chile, so while some travelers may bus in from Uruguay, Argentina or Venezuela, others arrive via the trem da morte (death train) - named after the fate that befalls many who hitch a ride on the train's roof - from Bolivia.
By river, many travelers take a slow boat along the Amazon from Iquitos in Peru or into the Pantanal via the Rio Paraguay from Asunción, Paraguay.
Flying within Brazil isn't cheap, but the huge size of the country makes taking at least a couple of flights almost a necessity. Compare prices online, then find a representative travel agent; otherwise, if you plan to take more than a couple of internal flights, a Brazil Airpass is a money-saver though it is time-restrictive. The domestic departure tax is often included in the price of your ticket.
Except in the Amazon Basin, buses are the primary form of long-distance transport for most Brazilians, and services are generally both excellent and punctual, with all major cities linked by frequent buses. Conversely, there are very few railway passenger services in Brazil. Enthusiasts should not despair however, as some wonderful touristic railway routes remain in operation, including the Curitiba-Paranaguá run.
Although river travel in Brazil has decreased due to the construction of a comprehensive road network, it is still possible to travel by boat between some of the cities of the Rio São Francisco and along the Amazon, where road travel is generally not a practical option.
Driving around Brazil is, ahem, an experience: it's anarchic and spectacularly dangerous, particularly at night, when livestock wander onto highways and potholes cannot be spotted. Though a convenient way to get to many parts of the country, driving should only be undertaken by those with tidy documents, adequate insurance and strong nerves for dealing with police. It goes without saying that Brazil is not the ideal country for long cycling trips, though some do attempt it.