From the website that has been setup to explain and document the project, as it progresses:

On April, 21st, 2012, Costa Crociere and the Costa Concordia Emergency Commissioner’s Office announced that the tender for the removal of the ship from Giglio Island has been awarded to Titan Salvage in partnership with the Italian firm Micoperi. The work begun in early May after final approval from the Italian authorities. The Concordia currently rests on its side on a downward sloping seabed, almost precariously balanced on the edge of a steep underwater hill. The 6 phase project involves building a scaffolding just below the Concordia, on the slope, that is anchored deep into the seabed. The Concordia will then be tiled upright again, so that it is resting on this new scaffolding. Once this is completed, cassions on the starboard side which will be used to re-float the ship. The site contains a plethora of 3D renderings of the phases of the project.