Costa Deliziosa was floated out at Fincantieri's Marghera shipyard March 12. Here in some amateur video you can see the beginning of the process. Fincantieri celebrates the occasion by breaking a bottle of champagne, then lots of water floods into the drydock, floating the ship up for the first time. There's lots of video here of water gushing, but as you'll see, it's a very slow process, usually taking about 24 hours, so in reality, there's not a lot of instant gratification. Eventually, the next day, the ship is towed out to a finishing dock where construction will continue, freeing up valuable space in the drydock so the construction of another ship can begin.
We have additional photos on the CND website.