By plane
The closest airports are at Pisa and Genova. Firenze is also a reasonable choice. The city of Milan is about a 2 hour train ride to Genoa where one is able to change to the local train line. Milan's Malpensa International Airport serves as a major intercontinental hub for the Italian airline Alitalia, but you will have to take a bus to the train station from the Malpensa Airport ~1 hour. There are also good connections from North America via large hubs such as New York City, Atlanta, and Philadelphia. Delta Airlines also operates a flight from Atlanta via New York's JFK International Airport to Pisa's Galileo Galilei International Airport.
By train
The Cinque Terre villages are well connected by rail and each of the villages has a train station, though some are only served by local trains. Regular local trains from Genova and La Spezia run with high frequency. All trains are operated by the state carrier, Trenitalia (http://www.trenitalia.it/...). When traveling from La Spezia, you can buy your passes for Cinque Terre in a tourism office in a hallway off of platform 1 at the La Spezia station.
By car
Take the 'litoranea' road from La Spezia. It takes approximately 20-30 minutes from La Spezia to drive to Riomaggiore or Manarola. There is a good parking garage in Riomaggiore, up the hill from the train station. The parking garage operates from 8am to 9pm. You will not be able to park in the garage after 9pm but may find a few open spaces near the parking attendant office. Parking is 23 Euros for 24hr. The roads to and between the five towns are not for the faint of heart, and why most travelers are encouraged to leave their vehicle in La Spezia and take the train to the Cinque Terre.