Eleanor, It depends on which city you arrive and depart as well as the duration of your stay in each town. Write back and we'll update our advice. I will try to help.
lake Como
Venice.
Let's assume you arrive in Rome and depart from Venice (or more likely Florence or Milan if you live in USA)
Trains, look for "Freccia" lines, also you don't have to book in advance for most trains unless you have to be someplace at a particular time such as a plane departure.
_Freccia train from Rome to Naples then local train (look for Circumvesuvia) to Sorrento. If you can afford to spend several days on the Amalfi Coast skip La Spezia/Cinque Terre later on in this schedule.
_Freccia train from Sorrento via Naples to Florence.
_Stay in Florence for a few days and visit Siena, Chianti, Assisi, Orvieto and the smaller hill towns of Tuscany either by tour or car rental if you are brave. You can do Siena and San G in one day but other than those two I would try for only one town a day. Do your homework and choose two or three.
_Car or Train to La Spezia (with optional stop in Pisa or Lucca), Stay in La Spezia and take the local train up the coast to the Cinque Terra towns.
_Train to Venice (You'll have to switch in Parma or Bologna so if you have time you can always stay overnight and see these famous food towns). You could also skip La Spezia and go straight to Venice on the superfast train (2hrs)
_Train and/or car to Milan/Lake Como. Obviously, I favor trains over car rental but for this portion I would consider a car so you can detour to the small towns along the Swiss boarder.
With this many train days you may want to contact Rick's travel advisors and talk about using a rail pass. I don't like them because of the prebooking required but they do save money. Warning they can be tricky so if this is your first time using trains you may want to stick with the buy as you go route.