By train
Bolpur is the railway station for Santiniketan. It is two to three hours by train from Kolkata. Convenient connections are 13017/13018 Gana Devta Express departing Howrah at 06:05, 3015/3016 Shantiniketan Express departing Howrah at 10:05 this is the only train which originates/terminates in Howrah and Bolpur, so one has a better chance of finding seats on this train rather than the other trains if one buys unreserved tickets. If you are buying reserved tickets, then it won't make a difference, 2347/2348 Sahid Rampurhat Express departing Howrah at 12 noon and taking only 2 hours 20 min - the shortest time , 3011/3012 Malda Inter-city Express departing Howrah at 15:25, 5657/5658 Kanchenjunga Express departing Sealdah at 06:45, 2345/2346 Saraighat Express, 215/216 Visvabharati Fast Passenger, 3071/3072 Jamalpur Express, 209/210 Darbhanga Passenger are other good trains.
For schedules check with Indian Railways (http://www.indianrail.gov.in/).
If you are female and taking the train, look for designated "Ladies Cars" to enjoy a more comfortable and hopefully less crowded ride. If you are travelling with significant amounts of baggage, be aware that even in reserved cars you may struggle for space, and hiring a car may be a better alternative to reach Santiniketan.
By bus
Santiniketan is well connected by buses from all around. From Kolkata, if you want to go by bus, then you have to take Kolkata-Asansol bus or Kolkata-Suri bus. For Asansol bound bus you have to get down near Panagarh and for Suri bound bus you have to get down near Ilambazar and for both cases you have to catch another bus for Santiniketan.
By car
Santiniketan is connected with Kolkata by an excellent road Around 60% road is excellent 4-lane freeway. But then around ~70kms starting from Panagarh is of narrow and bumpy roads with traffic jams round the clock. From Kolkata travel to Dankuni and take the Durgapur Expressway. It is now part of NH2. It will bypass Saktigarh and Bardhaman. At Panagarh Darjeeling Mor turn right. After the highway crosses the Ajay river take the road to the right at Ilambazar and proceed towards Bolpur. At the Santiniketan-Sriniketan junction also called Surul Mor take the road to the left. Santiniketan is 212 km from Kolkata by road. Good drivers can cover the distance in about 3 hours.