The best way is to board any bus that goes to Digha from Kolkata. Get off at Balisai and take a cab from there to reach Tajpur. It is better to book the cab before boarding the bus as getting a cab on-spot may be difficult. Or you may get off at the Digha Bus Stand and take a cab from there.
Another good option may be to go in a car, via Vidyasagar Setu, Kona Expressway, NH-16, and Kolaghat. From the Kanthi-Digha Road, there is a left turn that will take you to Balisai. From there the beach is hardly 2 km away. In Kolaghat and Mecheda, there are branches of some renowned restaurants where you may stop by for breakfast or lunch. The entire road trip might take 4-4.5 hours, depending on the driving speed and traffic.
Trains, though available, are not a popular choice to go to Tajpur. But if you want, take any train going to Digha (Kandari express, Pahria express, Duronto Express, and Tamralipta express) and get off at Ramnagar station. From there book a cab, preferably a pickup facility through your hotel.