The Vikings sailed from Iceland toward Greenland. Due to fog and wind they missed Greenland. Instead landed in Newfoundland.
Christopher Columbus was not expecting to sight land when he did. When he landed he didn't know were he was. He thought they were in India.
Ponce de Leon was the governor of Puerto Rico when he heard about the land in the north. When he sailed north he discovered what's now Florida. He was looking for the "fountain of youth." Magellan sailed around South America and across the Pacific. He was looking for new land.
Cartier left France to sail the New World. He had discovered the St. Lawrence he thought he had found the Northwest Passage. It wasn't until he sailed up the river when he realized he had found a river not an ocean passage.
DeSoto and his fleet of ships left Havana, Cuba. He landed in Florida and marched westward.
He found the Mississippi, but no gold.
Henry Hudson was looking for China; instead he found what is now known Hudson River. The next year Hudson sailed in an English ship and sailed farther north looking for the Northwest Passage. Hudson got put in a boat with his son & a few crewmen. The boy, men & the small boat were never heard from again.
Jamestown was established. It was the first English colony.