By train
The nearest train station to Gangtok is New Jalpaiguri in Siliguri which has direct connections to New Delhi, Kolkata, and other major cities in India. It is a 10-12 hour journey from Kolkata.
Once you arrive in New Jalpaiguri, you can either hire a taxi from the station itself or take an auto-rickshaw to the Siliguri bus stand. From there, you have the option of travelling to Gangtok by state bus, roughly a 5-6 hour journey.
Dozens of jeeps travel to Gangtok daily from Siliguri, Darjeeling, Kalimpong, and other mountain locales.Fare of the shared cabs is generally fixed, it is around Rs. 155 to Gangtok from NJP station. Drivers might try to charge high so check for the fare with other cabs before taking one. Approx. 95 kms distance gets covered between 2-3 hours.
By plane
The nearest airport is at Bagdogra,from there you need to hire a cab or taxi to go up there.A lovely highway with beautiful landscapes,twists and turns and loads of waterfalls and also you'll find River Teesta always running along.Many direct flights are there for Bagdogra and after reaching there its just the mountains and you.