As Frank has said, trains will be the best method for where you're going. This is the website for the Italian national rail service:
http://www.trenitalia.com/tcom-en
You will need to input the names of the destinations in Italian. I'm guessing you'll be flying into Malpensa? If so you'll want to take the Malpensa Express train to Milano Centrale, and a train from there to Pisa Centrale.
From there, you'll have to choose a town in the Cinque Terre (Monterosso, Riomaggiore, Manarola, Corniglia, Vernazza) or nearby (La Spezia, Levanto). BE AWARE? This is high season in the CT and booking started filling up month ago! I would not count on just landing into one of the 5 villages and finding a place to sleep. You may need to look in La Spezia or Levanto. Try to reserve something before BEFORE you go, and you will probably be limited to whatever has an open spot within your budget.
And then train from wherever you end up to Roma Termini.