The port of Citivecchia is where the ship docks, its 40 minutes by train to San Pietro station in Rome for the Vatican and just over an hour to Rome Termini, the central station.
We bought a travel pass from the newspaper stand inside the railway station (ignore the queue outside the station, they are queuing for the station ticket office). The ticket, which cost just 9 euros, gives unlimited travel on trains and transport from Citivecchia to Rome and in Rome itself.
The weather was very cool with odd spots of rain every now and then.
When returning from Rome, if you want a seat on the train I would advise you travelling from Rome Termini station, the starting point for the train. Leave plenty of time, as the platform is a good 15 minutes walk from the station entrance.