Italy is more formal than visitors expect in some ways and more relaxed in others. La bella figura — presenting yourself well — is a real social value, and being slightly smarter than strictly necessary is normal in restaurants, in churches and on the evening walk. Beachwear stays at the beach.
Churches enforce a dress code. Shoulders and knees covered, for everyone, at St Peter's, Venice's Basilica, Florence's Duomo and most working churches. Guards turn people away every day. A light scarf in a bag solves it permanently.
Meals have a structure. Antipasto, then a primo of pasta or risotto, then a secondo of meat or fish with contorni ordered separately, then dolce. You need not order all of it, but a primo is not a starter and a secondo will not arrive with vegetables unless you ask for them.
Say buongiorno on the way in. Greeting people when you enter a shop, a bar or a small restaurant, and saying arrivederci on the way out, is close to compulsory and its absence reads as rudeness. The bill will never come unprompted, because hurrying a table is considered impolite — ask for il conto.
Regional pride is not a joke. Food is the main battleground: carbonara belongs to Rome, pesto to Liguria, cotoletta to Milan, orecchiette to Puglia. Asking what the local speciality is will get a far warmer response than comparing it to somewhere else's version.
Finally, take the passeggiata seriously. The evening walk before dinner, done by everyone in their good clothes, is the most reliable way to see a town as it actually is. Small towns do it better than big cities, and it costs nothing.