PS:- u can take a car to DH, or catch any local train from Sealdah.Travelling by train takes one and half hours.
Government buses leave Calcutta from the Shahid Minar bus terminus throughout the day, going directly to Diamond Harbour.
Private buses leave from Babughat. Most Calcuttans, when travelling in groups, prefer to go to Diamond Harbour in cars or chartered...
more...

buses.

ADDING
Ganga Sagar is where the Ganges flows into the Bay of Bengal. Sagara Island is 105km south of Calcutta and about 64km (40 miles) south of Diamond Harbor, at the confluence of the Bay of Bengal and the Ganges. At this point the Ganges is about 24km wide.
Located here is the Kapila Muni Temple, in which Kapila Muni resides with Ganga­mata (the goddess of the Ganges) on his right and King Sagara (the great-great-grandfather of King Bhagiratha) on his left. It is said that the great sage Kapila Muni resides here...
more...

in trance for the deliverance of the conditioned souls.
West Bengal tourism organizes a boat trip to the Kapila Muni temple.
Every year on Makara-sankranti (mid-January), there is a large, three-day Ganga Sagar Mela Festival in which thousands of pilgrims come here to bathe, hoping to be liberated from rebirth. The bathing festival is literally attended by hundreds of thousands of people from all over India. This makes the festival an austere event. One person who attended told me that he slept only three hours in three days and had nothing to eat.
To get to Ganga Sagar during the festival, you must share a boat with one hundred people, although the boats are meant for twenty, then take a bus, a rickshaw, and then finally walk a good distance.
[SOURCE]