Our best suggestion is this: as soon as you arrive, even at the train station or at least at the front desk of your hotel, grab a copy of the local English-language weekly planner. This Week in Rome, Florence Today, A Guest in Milan are some examples. These will tell you what's on. You can ask the hotel concierge to see if tickets are available, or you can try a real Italian adventure, walk over to the box office and purchase the tickets yourself. But have someone call ahead and find out if anything's available first, or you may find yourself standing in a long line for nothing.
Another thing to keep in mind is that almost every city in Italy organizes an extensive summer activities program. The events, ranging from opera to theatre to movies to rock concerts, are almost always held outdoors and are great fun, even if you don't understand all the words. These schedules are as improvised as it gets, but they'll be listed in the weekly publications we mentioned above, and they offer a great way to unwind after a long hot day of hitting the cobblestones.
The most important thing to remember is this: don't stress out trying to arrange things before you leave home. Don't ever forget that the most Italian thing in the world is improvisation! Be prepared to take advantage of last-minute opportunities, which always abound.