Dave, Welcome to cruise chat!
Look at the "How to's of Train Travel in Italy" Post at the top of this section of the forum. You'll find the info you need in there.
It is not very far via train to Pisa form Liverno, but getting to the train station would be nearly impossible. They do run a shuttle bus to the town center where you can take bus route #1 to the train station. Or you could ask a taxi if they will take you to the train station. We had a group of 4 people that we shared a taxi ride with but it was still pricey.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013