At Rome airport, after baggage claim head towards exit, Celebrity Reps and crew will be waiting to check you off their list, (usually to the left as you exit baggage claim). They will take your suitcases and load into cages for transfer to the ship. The transfer will wait for other flights or until they have a full coach load you will then follow the rep for a walk to the waiting coaches. Keep all your travel documents etc with you as you wont see your suitcases again until onboard.
PS. It will probably be extremely busy as many cruise ships are often doing the same thing, but the reps are fairly obvious.