Netaji Subhash Chandra Bose International Airport (IATA: CCU) connects Kolkata with South East Asia and receives some flights from Europe. Most of the traffic towards Western hemisphere is handled by Emirates(Twice Daily) and Qatar Airways. New operators are coming soon. The domestic terminal, on the other hand, is among the best in India. It has undergone a major face-lift and expansion including a swanky new terminal,night landing facilities,etc to cope with the expanding bulk of air traffic and new airline companies popping up almost every month.
From the airport prepaid taxis, Ola and Uber are available.
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.
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.
You can find many cabs on the roads or you can always hire one from the numerous taxi stands strewn across the major cities. There are pre paid taxis also available at major railway stations and airports. You can also hire luxury vehicles from certain travel agencies