The Dutch colony of New Netherland became the English colonies of New York and New Jersey through military conquest and through treaties.
New Netherland was created as a Dutch colony in the 1610s. At this point, there was very little British presence in what is now the United States. Over the next 50 years, the British presence grew. When the Restoration of the Stuart monarchy happened in 1660, the British became more aggressive about colonial expansion and consolidation in North America. This led to a British expedition in 1664 that attacked and conquered New Netherland. The newly won territory became the colony of New York, which later split to become New York and New Jersey.
From 1664, these territories remained British almost continually. They were briefly retaken by the Dutch but the colony was then returned to Britain by treaty. From 1674 on, what had once been New Netherland was to be British on a permanent basis.
The British monarchy wanted to close the gap between their possessions along the Chesapeake and in New England. A British expedition in 1664 by the Duke of York seized the Hudson Valley and Manhattan Island from the Dutch. New Amsterdam was then renamed New York. The already present Dutch settlers were treated equally and were allowed freedom of worship. However the Duke refused to establish a representative assembly otherwise seen in Virginia or Massachusetts, which was met with fiery resistance amongst the colonists. The Duke yielded in 1683.
New Jersey was cut out of New York after the Duke of York believed the colony would be too large to monitor efficiently. He handed the reins to two of his aides, George Carteret and John Berkeley. The colonies of East and West Jersey were established with lucrative land, colonial representation, and universal religious tolerance. However constant bickering between land ownership along the borders between the Jerseys lead to them being consolidated into New Jersey in 1702.