There are no (more) trains in Surinam.
Car and bus
The international airport is situated at a considerable distance from the Surinam capital, at 45 kilometers south of Paramaribo. The airport is easily accessible by rental car, because it's located right off the Kennedy Highway which leads to Paramaribo.
There's also a bus connection between the airport and Paramaribo, but buses only run a few times a day. Bus company Le Grand Baldew (Tel. +597 474 713) in Paramaribo maintains a shuttle bus service with the airport.
Car rental Paramaribo Airport
You can find counters of car rental companies in the Arrivals Hall. Three rental companies are present at Paramaribo Airport: Avis, Budget and Europcar. 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.
Upon flight arrivals taxis are available outside the terminal. A taxi ride from the airport to Paramaribo takes about an hour and costs approximately 125 Surinam guilders.
There's a very small parking lot outside the terminal with space for only 12 cars. You don't have to pay to park here.