The answer to this question depends to a great degree on whether you include what is now Mexico in your definition of North America. If you do, the beginning of colonization in North America is very much a Spanish story. If you do not, it revolves largely around the English.
If we consider Mexico to be part of North America, the colonization of North America began around 1520. This was when the Spanish conquered the Aztec Empire and began to colonize in and around the Valley of Mexico. If we look only at the part of North America that is now in the United States, colonization did not begin for another century.
The causes of colonization also vary to some degree with the area of North America. The colonization of Mexico was caused by “God, gold, and glory” in some combination. This meant that colonists were looking for wealth, for power and fame, and to spread the word of God among the natives. (Again, not all of these motives were necessarily equally strong.)
By contrast, the colonization of what is now the United States was about money (in the Chesapeake) and about the ability to live according to the rules of one’s own religion (in New England). The English were not there to convert the Indians. They were there to set up their own English societies for economic and/or religious/political reasons.