The main gateway is Calama, which has an airport with regular flights from Santiago. From Calama it is about an hour by bus or shared transfer to San Pedro de Atacama, the main base for visiting the desert. Alternatively, you can fly into Antofagasta, Arica, or Iquique and travel south overland.
The Atacama also sits at a crossroads for overland travellers heading between Chile, Bolivia, and Peru. The border crossing at Hito Cajón connects to Uyuni and the Bolivian salt flats — a popular route done as a multi-day jeep tour.