If you have used a travel agent, Schultzie is right - they will be able to make all of your hotel/transfer arrangements.
I would urge you to fly in the day before (there are just so many things that can go wrong when flying in the day of a cruise). The airport is quite a ways from the cruiseport, therefore not too many hotels offer shuttle service. Here are a couple of suggestions, however: The Holiday Inn - Los Angeles/San Pedro Harbor offers a cruise package that provides free shuttle service from the airport to the hotel and from hotel to cruise port for a 1 night stay.
Or, you can locate a hotel near the airport and either take a taxi to the cruise port (can be expensive) or purchase the cruise lines transfers. That option will require you to return to the airport the day of the cruise, however. There are also airport shuttle services that provide transfers to the port (about $18 pp).
Hope these suggestions help-