Some may have gotten the wrong idea about Italian food from the many inauthentic adaptations found around the world, especially in America. Because we have traditionally been big meat eaters, we changed real Italian recipes to include meat, or increase the amount of meat (and cheese, and fats.) For example, spaghetti and meatballs is not an Italian dish, but Americans like it because they often feel cheated without some meat in their plate. Eggplant parmesan, which is Italian, is vegetarian, but all the variations such as chicken parm, veal parm, and so on, were created to appeal to meat-lovers. The classic pizza is vegetarian.
It is true that Italians are eating more meat than formerly, because Italy is now a rich country. But its long culinary tradition was based on the scarcity of meat and the ready supply of grains and vegetables. Thus, meat (and even fish) were usually included as an ingredient, often in small amounts, for flavoring. What this means is that it will be easier to adapt many non-vegetarian dishes by simply removing the meat or fish.
The classic pizza is vegetarian but not vegan, and my favorite pizza is an all-vegetable one. Pasta dishes are easy to make without meat or fish- there are oodles of recipes based on vegetables. One of the easiest sauces (and one of my favorites) is based on olive oil, garlic, tomato and fresh basil. Spaghetti aglio olio (with olive oil and bits of garlic) is yummy and vegan, not to mention cheap and easy and health. Pesto is vegetarian. Pasta salad with olive oil, veggies and herbs is delicious. The dishes can be made vegan by eschewing the cheese and butter. Risotti are also excellent with veggies (artichokes, radicchio, zucchini, asparagus, mushrooms...) and even fruit (strawberries, pears.) Minestrone is generally also vegetarian, and most frittate are vegetarian.
The traditional cuisine of Central and Southern Italy is even more vegetarian-friendly. Lots of pasta and bread, olive oil, beans, fruit, herbs. Many soups with pasta and legumes, or pasta and vegetables. Wine! Yes, if you are doing without meat or animal products in general, it would be wise to learn to cook with wine. A collection of fresh herbs is also a good idea. Don't forget the nuts.
Some ideas can be gathered from taking a look at my recipes (sidebar, right), which include a number of vegetarian and even vegan dishes.
In the picture, Il Cucchiaio verde (the green spoon), the most famous Italian vegetarian cookbook, which I have used and recommend. I don't think it's been translated, though.