How and why was the colony of New York founded?

In the early 1600s, the Netherlands threw off Spanish rule. The country then gave the Dutch West India Company control of Dutch trade in many parts of the Americas. The Dutch, freed and prosperous, wanted a share of the wealth flowing into Europe from the New World.
The Dutch West India Company claimed New York (then called New Amsterdam) and set up trading stations there. At first, the company goal was to profit from the lucrative fur trade. Later, it wanted to start agricultural communities to support its fur trappers and hunters to ensure a steady flow of furs into Europe. This meant establishing permanent farming settlements in New York.
Because the Netherlands practiced religious toleration and was a wealthy country, people had little incentive to want to take the risk of settling a wild, unknown land. Therefore, many of the early colonists in New Amsterdam were "Walloons," Belgians who had fled their own country to come to the Netherlands.
A desire for profit drove the Dutch colonization of New York. Later, the English were able to easily take over the lightly defended colony by sailing a fleet into the New Amsterdam harbor. The English, too, had as their goal colonizing the area for profit and as a way to help consolidate their holdings on the Eastern seaboard of North America. The colony practiced religious toleration, was home to some of the New World's first Jewish settlers, and had a high degree of European ethnic diversity.