Train travel is generally reliable, but can be confusing. The really fast trains called Frecciabianca are reserved 1st and 2nd class and travel between the major cities of Rome, Florence, Venice, Milan, Bologna, and Naples. InterCity trains are also reserved 1st and 2nd class that are the next level and are faster between larger towns. The Regionale trains serve all the stops, are unreserved, and are generally slower and often late.
Genova - (Genoa) between 1 hour and 2 hours
Firenze - (Florence) about 2 hours via Pisa
Milan - a little over 3 hours
Rome - between 3¼ and 4½ hours
Venezia - (Venice) between 4 ¼ and 5 hours via Milano
Pisa - about 1 hour
Lucca - about 1¼ hour via Viareggio
Parma - about 2 hours
Bologna - about 3 hours via Parma
Genova has two main train stations, Piazza Principe which is closer to the waterfront and has a shuttle bus to the airport and Brignole, which is closer to the shopping areas and old city.
Firenze Santa Maria Novella is the main train station in the center of the city.
Milano Centrale is the main station in Milano and connects to the metro as wall as the train to Malpensa airport.
Roma Termini is the main train station in Roma
Venezia has two train stations; Santa Lucia Train Station is the closest to the boat terminal.
Tips, tricks, and advice:
1. Always validate your ticket BEFORE boarding the train. There are small machines near all the tracks or near the ticket office. You can be fined or arrested for tickets not validated.
2. If you have a credit card with a chip, you can buy train tickets from the vending machines. This is particularly handy if the ticket window is closed or there is a long line.
3. There is a smart phone app called Prontotreno that is very useful for getting schedules, updates on departures, and even buying tickets.
4. Many larger cities will have a daunting number of train stations, so know which station you want. If you are not sure, just say Centrale (central).