Kolkata has India's oldest metro system, opened in 1984, running north-south through the city center. It is clean, cheap, and air-conditioned — a relief in the heat. The network has expanded in recent years and now includes an east-west line crossing under the Hooghly River to Howrah. For most tourist sights, the metro is the quickest option.
Yellow taxis (the distinctive Ambassador cars) still operate but are increasingly replaced by app-based Ola and Uber cabs. Auto-rickshaws serve fixed routes in specific areas. For short hops in narrow lanes, hand-pulled rickshaws — unique to Kolkata among major Indian cities — are still available in parts of north Kolkata, particularly around Chandni Chowk. Taking one is the most atmospheric (if complicated) way to move through the old city.
The Hooghly ferries are useful and scenic. Ferries run from Babu Ghat to Howrah and from Chandpal Ghat to the Botanical Gardens. For a few rupees you get one of the best views of the city across the river.