It is generally accepted that Christopher Columbus is the first KNOWN European to land in the New World. The Viking landings are unconfirmed and even speculation that a Welsh priest landed in the new world. The Chinese who are rumored to have landed on the west coast frankly didn't give a damn! Our ancestors who had crossed over the Bering Strait thousands of years ago were most likely unaware of their discovery. So, we cannot count the "native" Americans as the "finders" of the New World.
Here is a text on Columbus's first voyage to the New World.
The year 1492, on the evening of 3 August, Columbus left from Palos with three ships, the Santa Maria, Niña and Pinta. The ships were property of Juan de la Cosa and the Pinzón brothers (Martin and Vicente Yáñez), but the monarchs forced the Palos inhabitants to contribute to the expedition. He first sailed to the Canary Islands, fortunately owned by Castile, where he reprovisioned and made repairs, and on 6 September started what turned out to be a five-week voyage across the ocean.
A legend is that the crew grew so homesick and fearful that they threatened to sail back to Spain. Although the actual situation is unclear, most likely the sailors' resentments merely amounted to complaints or suggestions.
After 29 days out of sight of land, on 7 October 1492 as recorded in the ship's log the crew spotted shore birds flying west and changed direction to make their landfall. A later comparison of dates and migratory patterns leads to the conclusion that the birds were Eskimo curlews and American golden plover.
Land was sighted at 2 AM on 12 October by a sailor named Rodrigo de Triana (also known as Juan Rodriguez Bermejo) aboard Pinta. Columbus called the island (in what is now The Bahamas) San Salvador, although the natives called it Guanahani. The indigenous people he encountered, the Lucayan, Taíno or Arawak, were peaceful and friendly. He wrote with such awe of the friendly innocence and beauty of the natives that he inadvertently created the enduring myth of the Noble Savage. "These people have no religious beliefs, nor are they idolaters. They are very gentle and do not know what evil is; nor do they kill others, nor steal; and they are without weapons.".
No blood was shed on this first voyage; he believed conversion to Christianity would be achieved through love, not force.
On this first voyage, Columbus also explored the northeast coast of Cuba (landed on 28 October) and the northern coast of Hispaniola, by 5 December.
Here, the Santa Maria ran aground on Christmas morning 1492 and had to be abandoned. He was received by the native cacique Guacanagari, who gave him permission to leave some of his men behind. Columbus founded the settlement La Navidad and left 39 men.
On 15 January 1493, he set sail for home by way of the Azores. He wrestled his ship against the wind and ran into a fierce storm. Leaving the island of Santa Maria in the Azores, Columbus headed for Spain, but another storm forced him into Lisbon.
He anchored next to the King's harbour patrol ship on 4 March 1493, where he was told a fleet of 100 caravels had been lost in the storm. Astoundingly, both the Niña and the Pinta were spared.
Not finding the king in Lisbon, Columbus wrote a letter to him and waited for the king's reply, which requested that he go to Vale do Paraíso to meet with His Majesty. Some have speculated that his landing in Portugal was intentional.
Relations between Portugal and Castile were poor at the time. Columbus wrote to the King of Portugal, John II, and went to meet with him at Vale do Paraíso (north of Lisbon). After spending more than one week in Portugal, he set sail for Spain. Word of his finding new lands rapidly spread throughout Europe. He did not reach Spain until 15 March.