How did the english come in possession of new york?

Before New York was possessed by the English, it was controlled by the Dutch. Under Dutch rule, this territory was actually called New Amsterdam. 
Dutch Governor Peter Stuyvesant abdicates New Amsterdam, the capital of New Netherland, to an English naval squadron under Colonel Richard Nicolls. Dutch Stuyvesant hoped to resist English, but then he lacked manpower and his subordinates refused to support him. Following its acquisition, New Amsterdam’s name was changed to New York, in honor of the Duke of York, who organized the mission.