While there are no videos of the operation, it is likely that the SEALs boarded the ship in accordance with visit, board, search, and seizure techniques (VBSS). VBSS are the standard actions and tactics used by the U.S. Military to combat terrorism, piracy, and smuggling on the open sea.
This YouTube video shows a VBSS drill and demonstration conducted by U.S. Navy SEALs. The video is on the longer side, and we have summarized the actions taken in the drill below.
Navy SEALs rappel onto the vessel in three waves.
Screenshot / www.youtube.com
The first SEALs team on the ship take up defensive positions to provide cover fire as the other teams rappel onto the vessel.
Screenshot / www.youtube.com
Once all teams are on the ship, the helicopters fly out and maintain an aerial perimeter. At the same time, Navy SEALs in light boats flank the vessel being boarded.
Screenshot / www.youtube.com
Screenshot / www.youtube.com
Navy SEALs on the ship clear its perimeter, quickly making their way to the upper deck.
Screenshot / www.youtube.com
Meanwhile, SEALs board the back of the ship from their boats.
Screenshot / www.youtube.com
This two-pronged approach is meant to clear all hostiles on the vessel and reestablish command.
Screenshot / www.youtube.com
After the ship has been secured, SEALs leave the boat via makeshift ladders back onto their speed boats.
Screenshot / www.youtube.com
The full video of the drill can be seen below. As the video is long, we recommend starting it at 7:30.