Also worth mentioning is that trains are very frequent (some are continuing to Florence) but you MUST validate your tickets before boarding the train otherwise you could get a hefty fine. To validate tickets simply insert them into any of the small yellow machines positioned on the platforms so that the time and date are imprinted on the end. If you have return tickets then you validate the other end of the ticket when you come back.
Easy. We did livorno to Pisa at Easter:
1 euro each from cruise ship to centre of Livorno
1 euro each way bus from Livorno to the station, 3 euro return to pisa.
Bus from the crusie ship drps us of in the centre by an information kiosk. There is an archway leading past some shops, through there and cross the square. Take a number 1 bus to the station.
Train to Pisa took 15 minutes.
We walked from the station to the tourist office and picked up a free map. Then walked to the tower and back through the old part of town to the station.
Had a great day and as you can see, very cheap!