The public transportation, apart from the occasional strike, is fantastic in Italy. I guess they have to make up for not having Uber. (Although I’ve heard in some cities like Rome they do). Anyways, let’s look at the different options for getting from point A to point B.
Fast trains and local trains. Visit the train sites such as trenitalia.it or italo.it. (Change language to English) They have affordable fast trains connecting all the major cities. They also have slower, even more affordable ones the stop at more of the smaller towns along the way. Some trains, usually regional trains where you don’t choose a seat, require you to time stamp your ticket at one of the small ticket machines. DON’T forget to do this! Please ask an official if you are unsure. Otherwise you can face a fine.
Purchasing Tickets: You can buy tickets online or at the kiosks at the train station. Buying a few days in advance can save you sometimes 30 euros or more.
Again, linking most places. Try different nearby airports to see which fare is cheaper. For example, sometimes it is much cheaper to fly out of Pisa instead of Florence, and it is easy to take a 6 euro shuttle bus to the Pisa airport from Florence. (It leaves from the main train station, Santa Maria Novella)
While taxis can be seen everywhere. There are also certain taxi pick up spots, marked “Taxi”. Or, of course you can call the local cab company.