Any tips or advice for traveling from La Spezia's port to Pisa by train on our own?
Take the train to the Pisa San Rossore stop. It's just a five-minute stroll west of the Field of Miracles. Exit using the underpass of Piazza? Fancelli. Walk straight ahead to Via Andrea Pisano and turn left. Walk three blocks. You can't miss it.
Otherwise it is a 20 minute walk from Pisa Centrale. If you want to see more of Pisa then take the train here and walk.
Doris,
You can take a taxi from the port to La Spezia Centrale ( train station) & then follow the directions Christi has given you.
You may check the train schedules here: http://www.trenitalia.com
It takes about an hour to travel from La Spezia to Pisa S. Rossore.
If you plan to go up the tower, you may book your tickets in advance to avoid waiting in a long line:http://www.opapisa.it/en/tickets/buy/