There are two major railway stations in Kolkata - Howrah (not in Kolkata actually, it's in the adjoining city Howrah) and Sealdah. A new terminus station called 'Kolkata' has also started functioning since 2005, but presently it accommodates very few trains. Directly facing Howrah are ferries (Rs. 4) that can get you to the other side of the river either Babu Ghat or Fairlie Place from where you can arrange onward transportation with anything from taxis to public buses to human rickshaws. With the traffic situation this might actually save you time as well as money.
The Foreign Ticket Office is on Fairlie Place (with the main GPO on your left, take the next left - the office is a few minutes walk on the left) - very helpful and efficient service.
Kolkata is well connected by rail to almost all the big stations in India and also serves as the gateway to the North Eastern India.
If you are coming to Kolkata by trains using Sealdah station, you may prefer taking a pre-paid taxi to enter the city. The pre-paid taxi stand is just outside the station's main entrance. The counter is under a tin shade. Pre-paid taxis are reliable and will save you money and also the bargaining hassle.
However beware of touts who would claim themselves to be running pre-paid taxis. Always collect the receipt from the counter first. The receipt has two parts - one part is for your reference and the other part you will need to handover to the taxi driver only after you reach your desired destination. The Taxi driver will get his payment by submitting or producing this other part to the Pre-paid Taxi counter.
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Based on a work at Wikitravel.org & Traveldudes.org.