The best way to get around Kolkata is definitely the metro. But, Kolkata’s Metro Railway does not connect the entire city, yet. Here you will find Kolkata Metro Railway map and Metro Schedules and prices. There are auto rickshaw stands near most metro stations. Be advised that autos in Kolkata are only available for point to point transfers. They do not run on meters. Kolkata Buses are very frequent and connect the city very well. If you want to get to a point that is not connected by metro, you could either take a bus or a taxi. Here you will find the Kolkata Taxi Fare chart and a guide on how to calculate Taxi fares in Kolkata (which I still find quite painful). If taking a taxi from the Airport, Howrah Station or Sealdah Station, you must always take the prepaid ones. 24 hours radio cabs are most convenient for late night transfers to the railway stations and the airport. Kolkata is the only city in India which has trams, so you must not miss the opportunity.Take a look at the Ferry Service too.
Look here for Kolkata City Map.
If you need further guidance on how to get to a particular place in Kolkata just leave a comment here and I am sure you will get back many useful answers from our fellow Calcuttans!