How did the Dutch colony of New Netherland turn into the British colonies of New York and New Jersey?

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.