Italy has 2 large international airports and 25 airports for flights within Italy and Europe. Intercontinental airlines mainly arrive in Rome and Milan, with Rome being the main international gateway into the country. There are two international airports in Rome: Fiumicino (FCO - Leonardo Da Vinci) and Ciampino (CIA) for budget airlines. Milan also has two international airports: Malpensa (MXP) and Linate (LIN). Many people choose to arrive in Rome and depart from Milan, touring the three principal cities of Rome, Florence & Venice in-between flights.
Instead of taking a direct intercontinental flight to Italy it may be cheaper and more convenient to buy a return ticket to one of the major European gateway cities like London, Paris, Amsterdam or Frankfurt and from there use one of the low-cost European carriers to get you directly to your destination city in Italy like for instance Bologna, Naples, Pisa or Venice.
You can get to Italy by train from most places in Europe. From London, Paris, Amsterdam or Brussels a popular option is the Eurostar high speed train, but there are other possibilities. To go to Italy by train is not necessarily cheaper than going by flight and it definitely takes longer, but it gives you an opportunity to experience different countryside and cultures of Europe. Travelling by train you'll also get to see a lot of the Italian countryside, perhaps arriving via the Alps into Venice or Milan. Always try to reserve Eurostar trains where you can make seat reservations and be guaranteed to travel on the most comfortable trains.
Italy borders on France, Austria, Switzerland and Slovenia. All borders are open (without passport/customs checks), but cars can be stopped behind the border for random checks. Most car hire companies in Europe accepts that you take a rented car into other European countries and you can even pick up the car in one country and hand it back in another, but make sure to arrange this with the car hire company when you book so you know exactly what you can do and what you can’t do with your hired car.
Along with the low-cost airlines, you'll also find a wide selection of low-cost bus companies operating services from numerous European countries into many various Italian cities. In fact, most tourists arrive in Italy by bus, and if you are a single-traveler and young or young at heart you'll find many companies that will offer basic, but good value services including overnight buses to save on accommodation costs. Many of these bus companies have pre-arranged deals with local campsites or hostels through which you can enjoy further savings once you arrive at your destination.
You can also get to Italy by boat. There are several ferries departing from Greece, Albania, Montenegro and Croatia. Most of them arrive at Venice, Ancona, Bari and Brindisi. Some regular ferry services connect the island of Corsica in France to Genoa, Livorno, Civitavecchia (Rome), Naples and North of Sardinia. Barcelona in Spain is connected to Civitavecchia and to Genoa.