There are frequent bus connections to Antofagasta (2 hours). There are also frequent overnight buses arriving from Iquique...arriving normally in the early morning hours. The bus company will let you sleep on the bus for a few hours until morning so there is no need to book a hotel or hostel. Warning there frequent reports of bags being stolen in the bus station. It is a common occurrence. Thieves apparently use distractions, such as asking you to be part of a photo, whilst another steals your bags. Be extra vigilant and keep passport, valuables and credit cards in a money belt.
There used to be a train to Bolivia, but it has stopped. You have to get in and out by road and air.
Calama's airport, Aeropuerto El Loa, is located just outside the city and serves numerous daily flights to Santiago, as well as flights to other Chilean cities in the north. Tourists from Santiago often fly to Calama, from which they travel to San Pedro by bus or rental car.
Calama is not large and most of the city centre can be covered on foot. Collectivos (shared taxis) run fixed routes and cost Ch$500, while buses, named with letters of the alphabet, cost about Ch$300.
Get a taxi in the city centre to Chuquicamata. It is an enormous mine open to the sky. There is a free tour to the mine, its worth visiting.
To see the mine you should first sign up at the local municipal tourism office. It's located a few blocks from the main plaza on Calle La Torre between Calle Vicuna Mckenna and Pedro Leon Gallo (more towards Mckenna and on your left hand side as you walk from the plaza). It's in a small building on a market-lined street so pay close attention or you'll walk right by it. They'll take your name and information and direct you to the taxi/collectivo stand that can take you to the mine as of 13:15 PM. The cost of the collectivo is 1500 CLP each way. The tour starts when a bus picks you up near the fire station and ends about 60-90 minutes later. The collectivo is waiting for you at Chuqui when the tour ends. The tour itself is free but you will be asked for a voluntary donation for the children's fund.
There's a small amusement park for children off the main square in town.
And you can go to the mall. There's a movie theater there, but be warned, all the movies are in Spanish.
Rent a 4x4 truck and go see Chiu-Chiu, Lasana, and the geysers de Tatio. For around 40,000 pesos, you can rent a 4x4 truck. Chiu-Chiu is about 35km North-East of Calama. There are intresting ruins, a lagoon, and some old churches. Lasana is a beautiful canyon winding through the desert. It's green and really different. Then, a several hour drive across the salt flats and through some VERY rugged roads brings you to the Geysers of Tatio. If you camp on the NORTH side of the geysers, and come down in the morning, you can get in for free (otherwise around 16,000 for a truck and four people). The geysers are at about 4,200 meters, and you hit abou 4,700 meters coming in from the north. In May it was VERY cold (our water bottles froze that night solid). A very cool experience.
Calama is the best place to stock up on essentials before heading into the Atacama. While there are small supermarkets in San Pedro de Atacama, there are better prices and a wider selection here.
Be vigilant about your stuff and never lose sight of any of your bags in public places like the bus station (for instance, waiting for a connection). The thieves work in groups and usually one will try to distract you while another grabs the bag when you've turned around. Also, do not leave valuables or bags in your car even for if you are just running into the grocery store. Thieves will commonly break windows in rental cars and steal everything. Even in broad day light with security guards in the parking lot.
San Pedro de Atacama is two hours away by bus.
The airport is a few miles south of the city. You can call for an airport shuttle to pick you up at 98162091 for Ch$3.000. An ordinary taxi is said to cost Ch$6.000. You can also consider to take a collective to the southern suburb, and walk or hitch hike the last km to the airport.