Scott and Amundsen took different, but very similar, routes to the South Pole. Their bases were both on the edge of the Ross Ice Shelf, which they called the "Great Ice Barrier." Most expeditions used to start here because the Barrier is a huge floating ice shelf. It's perfectly flat and easy to travel on. It's basically a giant, frozen bay that cuts deep into the continent, giving explorers a shortcut to the Pole. It's on the bottom of the map below. White is land, gray is sea ice.
Approaching the edge of the Barrier was like sailing into a 100 foot wall of ice.
Amundsen and Scott landed on opposite sides of the Barrier and, more or less, walked due south toward the Pole. Amundsen's route was about 100 miles shorter, but it was uncharted. Scott's route was longer, but had already been mapped, removing much of the danger, and equally as important, the anxiety of the unknown.
Below, Amundsen's route is on the left and Scott's is on the right. The Barrier, in gray, would be open ocean if it wasn't frozen solid. Where the Barrier meets the land stand the towering Transantarctic Mountains with the smooth high plain of the Antarctic Plateau behind.
The journey itself consists of three parts - the long, relatively easy trudge on the flat Barrier (~400 miles), the crossing of the Transantarctic Mountains (~100 miles), and the high-altitude Plateau journey (~300 miles). The crossing of the mountains is the shortest, but most dangerous leg.
Rather than climb the mountains, Scott and Amundsen used giant glaciers as their "roads to the pole."
Scott's Route: The Beardmore Glacier, previously mapped and climbed by Ernest Shackleton.
Amundsen's Route: The Axel-Heiberg Glacier. Never before seen by human beings.