We've not sailed Celebrity so can't speak to anything specific for them.
Tips for cruising generally would be:
1. Try to pack light and expect additional baggage on the way back since you will be buying stuff on excursions.
2. Check the weather closely. Look at average temps/rain for the region and pack accordingly.
3. Keep your ID's with you at all times. Make color copies of everything and keep them separate and safe.
4. Try to learn about local customs. I know that in Italy they frown on skirts/shorts and certain clothing in their churches, ones you may visit on excursions. Learn alittle of the local language ahead of time. The simple stuff like please, thank you, where is the restroom (watercloset), sizes like small or large (I think picolo is small in Italian ! )
5. Be very clear on the local time versus ship time...they are not always the same. Keep the number for the ship/port in case you are lost or late and may miss the ship. Take your cellphone and be sure you have international calling, even only for the duration of the trip.
6. DON'T MISS THE SHIP!!!
7. When in port locate the nearest shop/store/market and get some bottled water to drink while sigtseeing.
8. Try to stay on major roads and near groups of people. Don't wander off into neighborhoods off the beaten path.
9. Ships excursions are more expensive but safer. If you go off on your own you are responsible for getting bak in time. The ship will not wait for you, but they will if you are on a ship sponsored excursion.
10. Learn where the Embassy or consulate for your home country is in each port in case you have issues ashore.
Hope all this helps !!
Phil & Liz