Depending on where you fly into, those cities have large central stations that have the comfortable Eurostar trains. These make less stops at the smaller cities in between so it's a quicker ride to each city.

When you book online through Trenitalia, you can print out your ticket from the yellow self-service machines in the train station. If you buy online, you'll look for a record locater number, they refer to it as a PNR number in case you get in line at the station to talk to a train agent to get your tickets printed out. The self-service machines are pretty comprehensive and will take cash if you want to wait to buy your tickets in Italy. However, I've encountered some machines that kept my change! The lines for talking to a warm body can be long, so the machines are a nice alternative.

When you can, it might be good to reserve a seat. It's a few more Euros, but it helps prevent you from being stuck standing in the aisle for a two-three hour trip. If you are going now or in August, there'll probably lots of people crowding the trains.

If you fly into Rome FCO, you can take the Leonardo Express into Rome Termini train station for E9.50. From there, you can catch the Eurostar to the other cities. Like the other posters said, in Firenze, the main station is Santa Maria Novella which will be right in the middle of town. Firenze is so small that you can walk around everywhere. Also, Termini is a transfer point between the A and B metro lines. A three day tourist pass is E11.00 and that enables you to take the subway and buses, but not the regionale trains or express to the airport. It's great to cut down on some of the walking between the major sights, like getting from the Vatican to the Colosseo.

To get to Venezia, you'll look for Venezia Santa Lucia. You can then take the vaporetto, the water bus, to get around the islands. These are located outside the station. A three day pass is like E12.00 if I remember correctly. If you're rich, you can take the water taxi. The vaporetto is great because they go all around Venezia and it's a cheap sightseeing tour if you want to see different parts of the area.

In Firenze, we went to a great restaurant called La Spada. We had the combo meal for E25.00 per person and that included antipasti, zuppa, the main course, and dulce della casa. We were so stuffed after that!

One cool thing we learned was that you can change your train reservation at the yellow self-service machine if you wanted to leave earlier than your planned trip, or later. It's just a matter of availability.