There's no train connection with La Paz Airport.
Car and bus
The airport of the Bolivian capital is situated 13 kilometers west of the city center. The airport lies at the end of the Autopista La Paz-El Alto.
City bus 212 connects the airport with the center of La Paz. The ride takes 30-45 minutes.
Car rental La Paz Airport
You can find counters of car rental companies in the Arrivals Hall. Two international rental companies are present at La Paz 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.
You can find official taxis outside the Arrivals Hall. You'll also be approached by unofficial taxi drivers, but we strongly advise against taking your chance with them. A taxi ride from the airport to the center of La Paz costs approximately 50 bolivianos. There are also minibuses which you share with other passengers and which cost about 5 bolivianos.
At the terminal's open-air parking lot parking is free. The covered (and guarded) part is meant for long-term parking and costs 20 bolivianos per day.