The English took control of the French and Dutch territories in North America by military force or the threat of military force. They wanted this land largely for economic reasons.
When Europeans were first exploring and claiming parts of North America, both the French and the Dutch took significant areas of that continent. They mainly used it as an area in which they had the sole right to buy furs from the Indians, though there was some European settlement as well. The English wanted to get the Dutch and the French out of North America. They wanted to control as much of the territory as they could. This was largely for economic reasons. They wanted to trade for furs and they wanted to have places to put settlements of white people. It was also for political reasons in that the English wanted to have the largest and most powerful empire. They felt that controlling more of North America would help them in that quest.
The English used military power and the threat of that power to take the Dutch and French lands. The Dutch lands were easy to take as they were not very large and Holland was not particularly strong by the 1660s. The English were able to take the Dutch territory in what is now New York without having to actually fire a shot. They simply threatened the small Dutch garrison with a fleet and took the land.
Taking the French land was much harder as it was much larger and France was much more powerful. The English fought a series of wars against the French that involved fighting in North America. Finally, in the Seven Years’ War (known in US history as the French and Indian War), the English defeated France completely and forced France to withdraw from North America. In this way, the English took the French and the Dutch colonies.