The nearest major train station is also in Varanasi. The station, Varanasi Cantt is 6 kms away and is well connected to all the major cities in the country including Delhi, Mumbai and Kalkata. Varanasi does have a small train station, but not many trains stop here.
From Varanasi, you can hire a taxi or take a bus to Sarnath.
Railway Stations in Sarnath