San Pedro town itself is walkable — the central area around the plaza is compact, and most of the restaurants, shops, and tour operators are within a few blocks. For the surrounding desert, essentially everything requires transport.
Bicycles can be rented from numerous shops in town and are the standard way to visit the closer sites — the Pukará de Quitor (3km), the pre-Columbian village of Tulor (9km), and the various viewpoints around town are all easily bikeable on flat paved or graded roads. Most rentals include helmets and basic maps.
For the further sites — El Tatio geysers, Valle de la Luna, the Salar de Atacama, the altiplano lagoons — the standard approach is a guided tour. There are dozens of tour operators in San Pedro, from basic shared minibuses to private 4WD excursions. Quality varies; reading recent reviews before booking is worthwhile. Some travellers hire 4WD vehicles independently from Calama, which offers more flexibility but requires preparation and awareness of conditions.
Altitude is the key variable for planning your days. El Tatio (4,320m) and the altiplano lagoons (4,000m+) should not be attempted on your first day in San Pedro. The rule of thumb from most guides: one full day at 2,400m in San Pedro before heading higher.