You can reach the Cinque Terre by train (along the line Genova-La Spezia) with regional trains which stop in every station. That means that every town of the Cinque Terre has its own station: listed in direction Genova-La Spezia (north-south) the stations are: Monterosso al Mare, Vernazza, Corniglia, Manarola and Riomaggiore.
To check the official site of Trenitalia click here.
The train is surely the most comfortable way to visit the Cinque Terre and the ligurian Riviera. In each station of the Cinque Terre you'll find information offices of the National Park, where to get touristic information and publications and where to purchase the Cinque Terre Card, a special card issued by the National Park, including several services such as shuttle bus and usage of the blue path number 2
The train, surely the best means of travel to visit the Cinque Terre and be enchanted by the beauty of the Ligurian sea. From March 16th the 5 Terre Express train is in service to travel comfortably between La Spezia Centrale, Riomaggiore, Manarola, Corniglia, Vernazza, Monterosso and Levanto with a single single fare ticket, taking advantage of the offer of 100 trains a day, 7 days a week, every 15 minutes