Mathura is an important railway junction. Most trains between Delhi and Agra stop in Mathura. The journey from Delhi takes 2-3 hours depending on the train type, while from Agra the trip takes about one hour. Most of the south bound and west bound trains stop at Mathura. August Kranti Rajdhani Express 12950/12951 (for Mumbai) for Delhi stops at Mathura. Other than that almost all major trains from Delhi and Agra stop at Mathura. It is well connected to national capital Delhi, state capital Lucknow and all major cities by rail.
From Sultanpur/Varanasi/Lucknow you may take train 13237/13239 Patna-Mathura.