The Grand Canyon Railway leaves Williams, AZ at 10:00am and arrives at the Grand Canyon at 12:15p. It then leaves the Canyon at 3:30p and arrives back into Williams at 5:45p.
After being used to Amtrak I found the steam train to be annoyingly slow and the ride was not all that scenic. The staff on the train was superb but the train was crowded and overpriced. The GC Railway will sell you a bus tour w/ lunch to take up your time once you're up at the Canyon; it is okay but nothing special.
I think Open Road Tours' own tour directly from Flagstaff is the best bargain and will allow you to see more and better parts of the canyon. However, if you choose to try the GC Railway steam train, Open Road tours has a shuttle that will take you from Flagstaff to Williams to catch the train (a 30 minute ride scheduled specifically to meet the train there) and has a convenient return shuttle from Williams Depot back to Flagstaff's downtown at the Amtrak Station.