The French and Indian War was a battle between the British and French (with the help of natives) on the North American continent. This was spurred by disputes over land claims. The British won the war easily due to the fact that they had a lot more men, because they were colonizing and starting families, while the French were just focused on making money.
A group of deeply religious people, known as pilgrims, were given permission to settle near Jamestown. With no exact reason known, they landed not near Jamestown, but in Massachusetts. There they started the second English colony, Plymouth.
In 1606, a company run by English investors, received permission from King James to establish a colony in North America. In 1607, with three ships and around 100 settlers they landed off the coast of Virgina. There they started the colony of Jamestown, named after their king.
Pizarro met the Incan ruler Atahualpa, and his priests, wanting to convert natives, handed him a bible. Atahualpa slapped it away, because he is "god" you don't hand, but offer. Pizarro offended, kidnapped Atahualpa. For his release, Atahualpa offered a room once filled with gold, and twice filled with silver. After receiving this, the Spanish strangled Atahualpa, killing the Incan leader. Leaving a demoralized empire behind, Francisco Pizarro and an army of about 120 men and 20 horses, conquered the empire, defeating the Incan army of around 30,000.
Cortes, sailing for Spain, landed in Mexico. Once there he heard about the large and extremely wealthy Aztec Empire. Cortes and his army of 600 men traveled to the Aztec capital of Tenochtitlan and were met by Montezuma II, their emperor. Montezuma believed that Cortes was a god and gave him a large amount of his gold. Cortes realized just how rich the Aztecs were and was not satisfied with a portion, he wanted all of it. With the help of native groups, advanced weapons, and most importantly, disease, the Spanish was able to conquer the Aztec Empire.
The first enslaved Africans to arrive in the Americas, came over due to Bartolome de Las Casa. He saw how poorly the Natives in America were being treated and came up with the idea to bring African slaves to the Americas, because they originally had rights. Once in the Americas, the European settlers took away all their rights/privelages. This led to a boom in the slave trade and increased success for European colonies.
Christopher Columbus set sail for the Spanish with the goal of reaching the Indies. After sailing only a few months, Columbus and his ships, the Nina, the Pinta, and the Santa Maria, unintentionally landed on what is now South America. Columbus, unknowingly, had opened up the New World for future European colonization.