There are no airports or railway stations in Sikkim. The only way to enter Sikkim from rest of India is by road using bus or jeep from West Bengal.
By train
Construction of a 50-km rail link from Sevoke, West Bengal to Rangpo, Sikkim started in 2009, but is not expected to be ready until 2015, and it'll take another few years until it reaches another 40 km to Gangtok.
Meanwhile, the nearest railway stations are Siliguri and New Jalpaiguri. Both of these have a number of trains connecting them to Kolkata. You should be able to get pre-paid taxis to Gangtok outside the railway stations easily.
By bus
The Sikkim government has fixed rate and fixed schedule buses plying between Siliguri and Gangtok.
After 44 years of closure, the Nathu La pass to Tibet, China â a part of the historic Silk Road â opened again in July 2006. There are plans for a Gangtok-Lhasa bus service.