All ticket machine have a built-in validator, so there is no excuse. However, if you buy it from a ticket office, the staff will not validate it for you - you must remember to do this yourself.
In comparison to most other European countries, Italy's subsidised public transport system is one of the cheapest. This page will describe how to use the system, particularly in hidden Italy.
If you remember nothing else from this page than this facts, it may benefit you in the future. In Italy it is possible to buy tickets in advance, since the prices are generally the same as if you buy it on the same day. To control people having a ticket which they might be tempted to use again, it is strictly necessary to validate your ticket before boarding your train. This is done by inserting the ticket (either end) into a small yellow machine on every station concourse and at most platforms. It stamps the name of the station, plus the time and date. If the ticket checker on the train finds you with an unvalidated ticket, s/he can charge a penalty fare and sometime prosecute.
Top Tip: Most Italian railroad stations have two types of timetable showing arrivals (Arrivo) and departures (Partenza). It is easy to read the wrong one in a panic! Likewise, some smaller stations show the timetable for a second station (typically a connecting station), so check the name of the station at the top of the timetable.
More advice: The timetable will tell you when your train arrives or departs and also provides the platform (binario). Do also check electronic boards for unscheduled changes.