There's no train connection with the airport of the Cuban capital.
Car and bus
Havana Airport is situated 15 kilometers southwest of the city center. The terminal is easily accessible by rental car. The Avenida de la Independencia (also: Avenida Rancho Boyeros) runs from Havana's center to the airport.
Local buses run between the airport and Havana's center, but you can only pay with so-called non-convertible pesos, which (officially) aren't available to foreigners.
Car rental Havana Airport
You can find counters of car rental companies in the Arrivals Hall, but there are only local rental companies present at Havana Airport, including Cubanacar, Fenix, Rex, Transtour and Via Rent-a-Car.
Outside the Arrivals Hall you'll find cars of Taxi OK (Tel. +53(0)7 877 6666) and Panataxi (Tel. +53(0)7 555 5555). Taxi OK charges higher rates than Panataxi, but when you leave the terminal you are not given a choice. You simply have to take the first taxi. A ride to Havana's center costs approximately 20 convertible pesos.
There are two parking lots, a large one outside Terminal 3 and a smaller one outside Terminal 2.