There's no train connection with the airport.
Car and bus
Santos Dumont Airport is situated only two kilometers from Rio de Janeiro's center, right on the Baia de Guanabara. The airport is easily accessible by rental car, because the road along this bay also runs past the airport.
There are two bus companies with connections from Santos Dumont Airport. The Realtur buses take about twenty minutes to run from the airport to the beaches of Copacabana. Every half hour, Real Auto Ônibus shuttle buses leave for the central bus station in Rio de Janeiro, Galeão Airport and the city's southern suburbs to its terminus Barra da Tijuca.
Car rental Rio de Janeiro Santos Dumont Airport
You can find counters of car rental companies in the Arrivals Hall. Two rental companies have a presence at Rio de Janeiro Santos Dumont Airport: Avis and Hertz. You can also book a rental car in advance using the service provided by EasyTerra; they compare the rates of several providers in a single quote.
There are taxis outside the Arrivals Hall for which you buy a ticket at a fixed rate at a kiosk. A ride from Santos Dumont to Ipanema costs about 30 Reals.
There's a parking garage near the terminal; you can also park your car at an open-air parking lot. In total there's space for over a thousand cars. You can get more information about parking at Rio de Janeiro Santos Dumont Airport via the Multipark website, or via telephone number 0800 116 001 (only within Brazil).