Descending to the bottom of the Grand Canyon yesterday took me through several layers of rock. They were laid down over a span of nearly two billion years. The canyon was carved into that rock much later.
To understand how this happened, you need to know about three events. First, the land uplifted to create tall mountains.
Then, a river system formed to the north and would become the Colorado River. Starting at a much higher elevation, the river gained enough power to cut deeply and continuously through those uplifted mountains as it flowed south and west toward the Gulf of Mexico. The water's flow became more powerful as it picked up sediment, working as an abrasive tool to carve the Grand Canyon.
This action alone didn't widen the canyon and make it what we see today. The third event was a series of several geologic actions: erosion, freezing and thawing, and chemical weathering. These caused steep canyon walls to collapse. Tributary streams also formed, and they carved side canyons and undercut some of the walls.