Obtain a passport. Traveling to Italy from the United States requires a passport. Start the process several months before June because rushed passports are more expensive.
Purchase air fare and book rental cars and hotel rooms. Be prepared to pay extra because it is the peak season. Search early to get better deals and compare prices on several sites. Book hotel rooms near popular tourist destinations in advance because they can sell out.
Make reservations for events and destinations in advance if possible. Some events might be sold out, and having a reservation might help you avoid long lines at other destinations.
Pack for the trip. June in Italy has average temperatures in the 60s and 70s, and the month also isn't particularly wet, so pack shorts, slacks and long sleeve T-shirts. Bring a sweater or sweatshirt for chilly evenings.