Vikings arrived in North America before Columbus sailed across the ocean blue in 1492. However, by the time the Vikings got here, they found the continent already settled by prior immigrants. The first humans to reach Virginia arrived when sea levels were much lower. The Native Americans arrived 5-10,000 years before the Chesapeake Bay developed, as sea levels rose after the glaciers melted.
We don't know for certain how Virginia was first settled. Those first Virginians may have walked here - but one theory is that they sailed here during the Ice Ages. Sailors could have entered Virginia from the east, hunting seals and catching fish as they following the edge of the frozen ocean. That might explain how the Clovis points found in Virginia most closely resemble stone tools that were developed near Solutré in southern France, rather than technology found in Siberian archeologic sites.

Another theory suggests some Asian hunters reached the West Coast in boats or rafts. The islands in the Pacific, including Hawaii, were settled by people who used some navigational technology to direct their journey by sailing or paddling, or were just lucky to find land after drifting to the islands on rafts.
The gap between Russia and Alaska is covered with water now, the Bering Strait. During the Ice Ages, however, sea level was hundreds of feet lower because so much water was trapped in glaciers, and there was a land bridge connecting the two continents. The general scientific consensus is that Asians crossed to North America and the genetic stock that settled Virginia originally was derived from the hunting groups that moved across that land bridge, walking east and south.
Global warming and global cooling have caused the shape of the continents to vary. The Atlantic Continental Shelf east of the Coastal Plain was exposed 18,000 years ago when the ice sheets covered Canada and parts of the United States south to Pennsylvania. When the glaciers and ice caps locked up vast amounts of water at the maximum extent of the Wisconsin glaciation, Virginia extended much further to the east.

As the ice slowly melted and sea levels rose, Virginia's Atlantic Ocean shoreline shifted to the west. The first Native Americans in Virginia arrived before the Ice Age ended, and they had to keep moving as river valleys on the Continental Shelf flooded and the Chesapeake Bay formed.
Sea levels are still rising. The land along Virginia's coast may also be sinking, due to geotectonic causes that are not fully understood. As a result, the Chesapeake Bay will expand and more of the Coastal Plain will gradually be covered with water. Barrier islands are migrating westward. If that pattern continues over the next few centuries, Tangier Island will be completely inundated and low-lying cities such as Norfolk will have to build massive flood walls... or people will have to migrate inland. If the Atlantic Ocean rises and "trangresses" onto the Coastal Plain, it won't be the first time that changing sea levels have altered settlement patterns in Virginia.
However and whenever they arrived, the Native Americans in Virginia were a low-tech culture compared to modern-day Virginians. The American Indians in Virginia walked across the state for perhaps 10-15,000 years. They created a network of paths, where they travelled regularly from their towns to good territories for hunting and fishing and gathering of wild foods. Paths also connected their towns, located near good drinking water and agricultural land - and the easy fords across the rivers.
The Native Americans who greeted the Jamestown settlers (or the Spanish who arrived 37 years earlier...) did not use the wheel, or have any horses. In 1607 the Virginians had no airplanes, no Metrorail or Virginia Railroad Express (VRE), no Omnilink or Fairfax Connector bus, and of course no cars. Still, you don't need much imagination to assume that the first Virginians explored all the gaps for crossing over mountain ranges and also climbed all the mountain peaks. Even if later Europeans did not document marked trails to the tops of Virginia's mountain peaks, there were no "first ascents" in Virginia by anyone who arrived after 1607.
No Native American in Virginia travelled on a horse before the Europeans arrived. Modern horses were introduced to North America by the Spanish and other Europeans who colonized the New World after 1492. There were no horses in Virginia between the time humans settled here and the Europeans brought horses. (Like starlings and honeybees, modern horses are a European species that reached America only after Columbus. The wild horses on the barrier islands - described to many young readers in Misty of Chincoteague - may have been survivors from Spanish shipwrecks in the 1500's, but are probably horses that escaped from (or were abandoned by) early English settlers.

To get around for about 10,000 years, the Native Americans in Virginia walked or paddled in canoes. The Native Americans in Virginia had no sailing ships, but they were using canoes routinely when the Europeans like John Cabot sailed along the North American shoreline at the end of the 15th Century.
By 1607, Powhatan's power extended across the Chesapeake Bay to the tribes on the Eastern Shore. It was physically possible to walk from "Powhatan's flu" northward, around the tip of the Chesapeake Bay to the Eastern Shore, and down to what the English labelled Cape Charles in 1607 - but Powhatan did not control much land north of the Rappahannock River. To get from Werowocomoco to the Eastern Shore part of Tsenacommacah, Powhatan's people used canoes to cross the Chesapeake Bay.
The Algonquians built those canoes with stone and bone tols, plus fire. Cutting a large standing tree with just stone tools theoretically was possible, and would have allowed the Indians to select the most desirable tree trunks - but the investment in labor would have been immense. There was a more reasonable way to find a suitable log for shaping into a canoe.
On occasion, floods brought a supply of trees to the boatmakers. The floods eliminated the hard work of cutting big trees in the forest with stone/bone tools, then somehow dragging the giant trunks to a waterway (in a culture that had no wheels for transportation). The Native Americans selected the best trunks from the intermittent flood logjams, and then converted those trunks into canoes. After all, the flood-provided trees were already cut and on the shoreline - would you go into the forest, select a tree, cut it down, and drag it to the river if there was a canoe-in-the-making already floating on the water?
The Native Americans used fire together with stone tools to excavate the excess wood and shape the tree trunk into a canoe. That would have required skill as well as patience. Making a canoe in Virginia before the Spanish, French, Dutch, and English arrived would have required a month or more of work. Those boats were manufactured with Stone Age tools, until the Europeans arrived and brought iron and steel. The Powhatans made canoes from trees, burning and scraping away the charred wood with sharp stones or shells until the trunk had been hollowed out.

hand-carved canoe at Jamestown, made by burning the wood
in the center and scraping the charred wood with bone and stone tools
(protecting the edges with mud, so they did not burn)
How do you burn a tree so it ends up as a canoe? Coals would be placed on the section of tree to be removed, charring the wood and making it easier to scrape away. But how did the canoe makers avoid burning sections of tree trunk that were not to be removed? Mud, good ol' Virginia mud. Mud was plastered on the edges of the trunk, ensuring that only the sections intended to be removed would burn. A thick layer would be slathered carefully on the edge of the tree trunk, and it would stop the fire from weakening the portion of wood that was being retained.