West Bengal's internal transport is reasonably good, with trains doing the heavy lifting between major cities and towns.
By train: The Indian Railways network covers West Bengal well. From Kolkata, frequent trains reach Darjeeling (change at New Jalpaiguri), Durgapur, Asansol, Bardhaman, Krishnanagar, and Nabadwip. The narrow-gauge Darjeeling Himalayan Railway (the Toy Train) runs from New Jalpaiguri up to Darjeeling via Kurseong; this is itself a reason to visit, listed as a UNESCO World Heritage site. Journey time is around 7 hours. Faster road transport cuts this to 3–4 hours.
By road: State and private buses connect cities across the state. Long-distance buses from Kolkata serve Darjeeling, Siliguri, Durgapur, Digha, and most other towns. For the coast — Digha, Mandarmani, Shankarpur — buses from Kolkata's Esplanade or private cars are the standard option. Shared taxis and jeeps are common in the hill areas around Darjeeling and Kalimpong, connecting towns that trains don't reach.
By ferry: The Hooghly River is still a working waterway. Local ferries cross between Kolkata and Howrah and connect riverside ghats. For Bakkhali, you cross the Hatania Doania river by ferry from Namkhana. In the Sundarbans, boats are the only way to move between islands.
Within Kolkata: The city has a metro (the oldest in India, opened 1984), buses, trams, and the famous hand-pulled rickshaws of Shyambazar. Taxis and auto-rickshaws are plentiful; app-based cabs (Ola, Uber) operate widely. The metro is by far the fastest way to move north–south through the city.