As you are aware, there are several 'answers' to this question -- based on different world views.
These answers range from taking millions of years to carve the canyon to a more rapid formation due to water run off in a more recent time span.
Perhaps the best explanation is the one presented here --
Dr. Andrew Snelling (PhD in Geology) explains in a 4 minute 17 second video.
This video is part of a DVD series. You may want to get the series, but in the meantime
HERE'S THE LINK to When and how did the Grand Canyon form
