1. They colonized them. There were differences in the way that colonization was done but in essence they would go to the Americas and proclaim that the land was their and they would start building settlements and expanding. Some were more vicious such as the Spaniards but some were less like the French. As they expanded they took more from the Natives.
2. The differences were mostly organizational. Spaniards got all colonies under the rule of the King and they would massacre anyone who opposed this and they spread rapidly. English people opened colonies for various reasons such as trading, or religious freedom, or similar, and they also had laws that prevented too much expansion. French mostly cooperated with local Natives and traded with them giving them things like clothes or guns or similar in exchange for help during exploration and help with hunting.