Central Calama is small enough to walk in 15 minutes end-to-end. The plaza, the cathedral, and most of the hotels and restaurants sit within a few blocks of each other. Taxis are cheap and plentiful; Cabify and Uber operate but coverage thins after dark.
For trips out of town — Parque El Loa, the Chuquicamata mine, the airport — taxis or rideshare are the easiest option. Car rental is available at the airport and is worth considering if you plan to combine Calama with the wider Atacama; the road to San Pedro is paved, but most other routes require a 4×4 and decent navigation.