Wikitravel.org has some ideas, which I've collected and grouped together below. It covers mainly respect, religion, clothing, and advice for women.
Italy has a reputation for being warm and welcoming and Italians are
uncommonly friendly and laid back, as well as very used to interacting
with foreigners. If you are polite and civil you should have no
problems, but don't expect that the average Italian speaks or even
understands English (except for young people). Also, it is not typical
in Italy for people to introduce themselves to newcomers: you will
have to introduce yourself to others. It is not rude but is just not
Italians greet friends with two light kisses on the cheek. Males do,
too. To avoid ending up kissing on the lips note that you first move
to the right (kiss the other person on their left cheek) and then to
the left. Even if you're merely acquaintances, this form of greeting
is usual, both on arrival and departure. When groups are splitting up,
expect big delays as everyone kisses everyone else. On first
introduction a handshake is usual, although not necessarily the firm
businesslike shake other nationalities may be used to.
In general, when joining or leaving a group, you will shake hands
individually with (or kiss, depending on the level of familiarity)
each member of the group. In the South, it is considered bad luck for
four people to shake hands (two and two) at the same time, forming a
cross. You will see Italians, especially older ones, pull back from a
handshake and wait to shake your hand until the other handshake is
finished, to avoid this.
If your cultural reserve makes you feel uncomfortable with this, don't
worry too much. The British in particular have a reputation for being
reserved, so you can always play up to this expectation, and Italians
will understand you don't mean to be rude. Handshakes are also
accepted greetings, and some Italians will kiss compatriots and offer
their hand to the awkward Brit.
To make friends, it's a good idea to pay some compliments. Most
Italians still live in their town of origin and feel far more strongly
about their local area than they do about Italy in general. Tell them
how beautiful their town/lake/village/church is and possibly add how
much you prefer it to Rome/Milan/other Italian towns. Residents can be
fonts of knowledge regarding their local monuments and history, and a
few questions will often produce interesting stories.
It's important not to judge people in return by their choice of
clothing. Styles do not necessarily carry the same connotations in
Italy that they would in Britain or some other countries. A woman in
fishnets, stilettos, miniskirt and full makeup at eight in the morning
is probably just going to work in a bank. Almost all youths lounge
about in skin-tight tee-shirts and casually-knotted knitwear (and are
very perplexed by the response they get when they take their sense of
style and grooming to a less 'sophisticated' climate).
Sometimes, clothing rules are written. To visit a church or religious
site you will need to cover yourself up; no bare backs, chests,
shoulders and sometimes no knees. Sometimes museums and other
attractions can also be strict; no bathing costumes, for example. If
you want to visit a church or religious site it's a good idea to take
something to cover yourself up with; for example a jumper or large
scarf. Some churches supply cover-ups, such as sarongs are loaned to
men with shorts so that they can modestly conceal their legs. Even
where there are no written rules, it's worth noting that bare chests
and large expanses of sunburnt skin are unacceptable away from beaches
or sunbathing areas, whatever the temperature is.
Sexual harassment is not regarded in the same way in Italy as in
English-speaking countries. The general atmosphere is pretty loose,
and women should be prepared for attention. However, the tone of this
'attention' is generally less aggressive than you may have read and
seen in movies. Men may call out compliments such as 'bella'
(beautiful) or, if you are lucky, 'bellissima' (incredibly beautiful),
as they did in the 1950s and 1960s. Bear in mind that this is still a
macho country and one until recently led by a man (Silvio Berlusconi)
who is famous for his associations with women. Men and women should
therefore expect to hear people saying things that would be considered
very offensive in other parts of Europe and North America.
Anyway, culturally, these comments are not seen as harassment; if you
respond angrily, everyone will be very surprised. Whereas women of
other nationalities may be used to telling strangers (in no uncertain
terms) to shut up and go away, in Italy, the norm is to ignore the
attention. In any case, responding in English or in imperfect Italian
will only encourage more attention. Do as the Italian women do, and
sail past with your head held high. If you avoid eye contact and don't
respond, you are extremely unlikely to be pursued or hassled further.