By fluvial erosion
Rivers are a very powerful erosional instrument. If it weren’t for marine currents that swipe clean continuously river’s estuaries their mouth would be quickly cloggend with the tons and tons of debris transported by their flow.
Their current actively excavate not only soil but also solid rock. The world is full of canyons resulting of their abrasive action. The Grand Canyon is only the most famous of them.
The depth and the time taken to dig a canyon are a function of the hardness of the bed rock. Canyons are generaly found in desertic areas where rocks are of continental origin.
These are softer and easier to excavate than igneous volcanic ones.