By train is the easiest way from Kolkata. The Shatabdi Express departs Howrah at 6:05am and reaches Durgapur non-stop in about 1 hour 45 minutes. The Black Diamond Express is slower (around 3 hours) but runs later. Numerous long-distance trains on the Howrah–Delhi main line also stop at Durgapur throughout the day. From North Bengal (Siliguri, Malda), take a train toward Kolkata and change at Burdwan, from where Durgapur is a short onward journey.
By road, from central Kolkata take the Durgapur Expressway (NH19). The journey is about 160 km and takes under 2 hours at off-peak times. The expressway is well maintained and the drive is faster than the train if you're starting from outside the city centre.
Durgapur has no commercial airport. The nearest is Kazi Nazrul Islam Airport at Andal (about 35 km away), which handles a limited number of domestic flights.