There's no train connection with Caracas Airport.
Car and bus
Caracas Airport is situated 21 kilometers northwest of the city center. The Venezuelan capital is easily accessible from the airport by rental car. First you follow the signs Autopista/Caracas (the autopista is a toll road). Next you drive through two tunnels (Boquerón I and Boquerón II). Then keep to the left when you reach the third tunnel (La Planicie), in the direction Petare.
Buses from the company UCAM (Tel. +58(0)212 352 4818) leave from the bus station opposite the two terminals to Caracas' center. Traveling time amounts to 40-50 minutes.
Car rental Caracas Airport
You can rent cars in the Arrivals Halls of both terminals. Eight car rental companies are present at Caracas Airport: three international rental companies (Avis, Budget and Hertz) and five local providers (Aco Alquiler, Amigo, Auto 727, Margarita Rental and Rojas). 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.
For your own safety it's best to hire a certified taxi. These can be recognized by a registration number on the side and a clearly visible identity card of the driver. There's a bright yellow desk of Corporación Anfitriones in the Arrivals Hall of both terminals where you can book a taxi. You can also do so online on the website Taxi to Caracas. Allow 30-60 minutes to travel to Caracas' center.
There are parking garages and uncovered parking lots at both terminals.