Very easy to DIY - go to google and type 'cruise ports call boards' - click on the first result will give you all the info under the 'Europe' section. Livorno is a huge port - take the shuttle bus to the town, then catch the #1 bus to the station and the trains run regularly and take around 15 mins. My guess would be just over an hour door to door. Have never seen any reference to taking the bus the whole way .
I have taken the bus to pisa, dont do it it takes ages you are much better off on the train, remember to get your tickets for the bus from the tobacconist, the bus goes from the central square, easy to do, you do have a bit of a walk from the train or the bus down to the tower, so be prepared for this.
Remember to validate your train ticket for travel before boarding by inserting it into the yellow box found on every platform. If you don't you could get a hefty fine. Once in Pisa it's about a 30 minute walk to the tower area (just walk straight ahead). This takes you through the centre of the city and is quite interesting once you get past the roadworks close to the station. Otherwise there are plenty of buses to take you there as Pisa local bus station is just outside the rail station.
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