Assuming you're not referring to the people who settled the Americas from top to tip...

The TL;DR

• Is there any truth behind the idea of pre-Columbian contact?

The Norse

The Norse emigrated from Iceland/Norway to the southwest coast of Greenland (Greenland is considered part of the North American continent physiographically if not politically) and stayed there for almost 500 years (~985AD - late 1400s). From there, the sagas mention forays to the nearby islands; findings across the Canadian arctic back this up, and Baffin Island is suspected to be the land referred to as "Helluland" in the Icelandic sagas. But most famously, the Norse Greenlanders established a short-lived settlement in what is now L'Anse au Meadows, Newfoundland, which is suspected to be the "Vinland" of the sagas. Here's the Parks Canada site; it's also a UNESCO World Heritage Site. The most important sagas that refer to these regions are the Saga of Erik the Red and the Greenlanders' Saga.

Some posts with general info:

• When did historians accept the Vikings' settlements in North America as fact?

• Why didn't the Vikings establish a permanent colony on Greenland or North America? - includes a handy map

• When the Vikings settled in Greenland & Vinland, they encountered the ancestors of the Inuit and more than once had skirmishes. Why did the Natives emerge victorious?

• Why did the Scandinavian peoples not inhabit eastern Canada to the same extent that they inhabited Iceland, Greenland, etc.?

• Why didn't the Vikings travel farther south than Vinland?

contact between Norse and aboriginal peoples:

• Do any Native American/First Nations peoples have any oral traditions or tales about the Vikings?

• Is there any record of Norse settlement in Native American oral tradition?

• What sort of interactions were there between Native Americans and Vikings?

• Do we know what actually happened during the Norse and Native American/Canadian encounters?

• Non-Saga sources describing interaction between Norse and Skraelings?

Other contact from the East

There have been a few claims but nothing has yet been substantiated.

• from the FAQ Travel and contact across the Atlantic before Columbus

• links to posts about the dissemination of knowledge What ever became of knowledge of Vinland and Leik Eirikson's discoveries by the time that Columbus set sail?

Contact via the Bering Strait

• Russia is so close to Alaska, why didn't the Russians discover North America well before Columbus?

• What interaction was there between indigenous peoples of modern-day Alaska and northeastern Siberia (Chukchi Peninsula) after the submergence of The Bering land bridge and prior to the 17th century A.D., if any?

• Did Alaskan natives have knowledge Asian peoples in Siberia before the colonization of the Americas?

Other contact from the West

• Did any East Asian civilizations before or during the European Age of Exploration explore the oceans to the east and is it possible that they reached the Americas?

• Are there any known or recorded instances of New World discovery or exploration in classical times?