Carson City has no commercial airport of its own. The nearest is Reno-Tahoe International Airport, about 30 miles north on US-395. From there it is a straightforward half-hour drive south.
By car from southern California, expect a full day's drive over the Sierra Nevada via US-395 or Interstate 80 through Reno. From the San Francisco Bay Area, take I-80 east to Reno and then US-395 south — roughly four and a half hours in good weather. Winter conditions on the mountain passes can add time and require chains.