Portofino has no train station. However, it is possible to take a train from Savona to Santa Margherita Ligure, the nearby town. From there you can take the public bus to Portofino. This option is very cheap, but takes a lot of time. Only do this if you have sufficient time.
There are direct trains between Savona and S. Margherita Ligure. The journey takes 1 hour 45 minutes to 2 hours and you pay € 6.60 per person (one way, 2nd class). The direct trains run not very frequent. Better check the timetable in advance.
Once you arrive at Santa Margherita Ligure train station, you can take the public bus to Portofino. Bus N° 82 runs every 15 minutes between S. Margherita Ligure station and Piazza della Liberta in Portofino. The journey takes about 20 minutes and costs € 1.50 per person. The bus ticket is valid for 100 minutes after validation. Check out the bus timetable before you leave.
TIP: buy your bus ticket in advance at one of the points of sale or at the ticket machine. On the bus, you pay double.
How do I get to the train station from the cruise port in Savona?
Savona train station is located in the west of the city at about 1.5 kilometers from the cruise port. If you want to walk there it will take about 20 minutes. A taxi ride takes half the time for € 15 per taxi (4 persons, one way).
A good alternative is bus N° 62. It runs every 30 minutes between the cruise terminal (Palacroisiere) and the train station of Savona. The journey takes 10 minutes. If you buy your tickets in advance at a Tabacchi kiosk it costs € 1,30 per person. On the bus you pay € 1 more. The ticket is valid for 90 minutes after validation.