According to a good friend (and retired Merchant Marine Chief Engineer) he theorizes (not likely) mechanical failure or (more likely) the ship was not loaded properly in-accordance to how the ballast tanks were filled. Furthermore, the craft left the port and took a shortcut in shallow water outside the main thru-way to save time. While navigating in shallow water, it likely executed a maneuver that caused a capsize because the ballast and loading were not correct.
As these ships are loaded/unloaded, there are supposed to be logs and checklists to be completed and the data is fed into a computer to calculate the ballast tank settings. Investigations will tell if procedure was followed.
How will they right this vessel? First they will secure/drain the fuel tanks etc... Then, cranes on barges will yank the cargo out of the top-most decks. Ballast tanks will be adjusted to favorable levels and many tugboats will pull it upright. They may need to make some fixtures as anchor points to hold the base of the hull as it's tipped back upright.
This is all theory from a guy with 35 years experience as a Merchant Marine with his last 15 years as a Chief Engineer. Reality may play-out differently...