How to go Mathura

By train

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 (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 3237/3239 Patna-Mathura.

By road

Mathura is situated between Delhi and Agra on National Highway 2, about 150 km south of Delhi and 50 km north of Agra. NH-2 is one of the best highways of country. Upcoming Taj expressway is in east of the city. Mathura is well connected to national capital Delhi, state capital Lucknow and all major cities by road. Many state transport departments busses are running through Mathura.

By air visit domestic flight details

Nearest airport is Agra (Kheria Airport). It is 50 km from Mathura. Perhaps most of the international and domestic flights are landing into IGI Airport, Delhi. IGI Airport is 150 km from Mathura. Upcoming new international airport will also be accessible via Taj expressway, 1½ hours from Mathura.
 

 http://en.wikipedia.org/wiki/Mathura