Calistoga is at the northern end of the Napa Valley, about 120 kilometres north of San Francisco. There is no train service to Calistoga.
By car is by far the most practical option. From San Francisco, take US-101 north across the Golden Gate Bridge to Highway 37, then Highway 121 north through Napa, and continue on Highway 29 north through St. Helena to Calistoga. Allow 90 minutes to two hours, more on weekends when Highway 29 through the valley can back up badly at the popular wineries.
By bus, VINE Transit operates local bus service within Napa County, connecting Calistoga with Napa city and St. Helena. The service is infrequent — plan carefully if relying on it. From San Francisco, VINE connects with BART at the El Cerrito del Norte or El Cerrito Plaza stations.
From Napa Airport (actually in Napa city, serving small aircraft only), a rental car is the only realistic option. The nearest major airports are San Francisco International (SFO) and Oakland International (OAK), both roughly 90 minutes by car.