You need a car or a hired driver. The wineries are strung along Highway 29 and the parallel Silverado Trail for about 30 kilometres of valley, and the gaps between them are too long to walk. Most visitors set out with a car and accept that the designated driver will not be tasting much; the better option is to hire a driver for the day, which is a Napa industry of its own.
The Napa Valley Wine Train, a restored train running between Napa and St. Helena, is a comfortable if pricey way to see the valley without driving — lunch and dinner runs include several winery stops. In St. Helena itself the town is easily walked end to end in twenty minutes.