There are many things we can say about how the Grand Canyon formed. For instance, the Colorado River carved the Grand Canyon. That's an answer that satisfies many, because the river is big, drains a large region, and lies at the bottom of the present-day canyon. It carries millions of tons of silt and sand downstream for temporary storage in Lake Mead before it ends up in the Gulf of California. The canyon is getting a tiny bit deeper and wider each and every day. That much is clear.
The gradient of a river is the relative slope of the river, the altitude it drops over a given distance along the riverbed. Higher gradient streams flow faster, and therefore tend to have greater erosive capacity. Since the highest gradients are often at the headwaters of a stream, erosion often acts to eat away at the edge of the drainage or plateau where the river originates. This upstream lengthening of the river is called headward erosion.
Check out the Google Earth image below of Bryce Canyon National Park. The famous hoodoos, or spires, form at the edge of the plateau and are light orange in color. The erosional amphitheaters represent the headwaters of the Paria River and other tributaries to the Colorado River. The amphitheaters completely surround a second north-flowing drainage, the East Fork of the Sevier River. The headwaters are carving away at the plateau edge, getting closer and closer to the channel of the Sevier River. In the near geologic future, the water that flows north towards Salt Lake City will instead flow southwest towards Las Vegas. Early settlers in the region took advantage of the impending piracy; they dug a canal that diverts some of the Sevier River into the Paria River drainage to support agricultural fields downstream.
Carving Grand Canyon: Evidence, Theories and Mystery, published by the Grand Canyon Association).
From 30 to 16 million years there was a dark period for which there is little evidence revealing the type of river activity. According to Ranney, the drainages became ponded, dry, rerouted, reversed, or "confused".
From 16 to 6 million years, basin and range style faulting severely disrupted the landscape, creating deep sedimentary basins that were isolated from one another. The sinking of these basins may have formed the high gradients that initiated deep canyon cutting, but until 6 million years ago, no Colorado River flowed of the Colorado Plateau at any particular point with any relationship to today's course.
Between 6 and 4 million years ago, the opening of the Gulf of California caused the integration of different river drainages into the unified Colorado River we know and love today. Much of the cutting of the Grand Canyon probably took place during this time period, aided in large part by extremely high river discharges fed by melting glaciers in the Rocky Mountains during the last ice age.