From Netaji Subhas Chandra Basu International Airport, you have a choice of cheap (really cheap) public mini bus transfer, or paying a bit more for a taxi.
Public transport in Kolkata is frightening, overcrowded, and falling apart, while taxis are merely frightening and falling apart.
Kolkata is the last place on earth that you can get old fashioned human powered rickshaws (not bicycles), and quite often these are the quickest way to get short distances because they are willing to dodge in and out of the traffic.
The main bridges tend to be congested throughout the day, so it you're crossing from one side of the river to the other, it makes sense to use a ferry.
