two weeks

Trenitalia is the main train company - servicing both fast trains between major cities and regional, slower trains to less major cities. Italo train is an alternative for fast travel between major cities but it will not get you to smaller ones. If you list where you're going, it will be easier to advise. If you don't want to bother looking between the two different options though, just focus on Trenitalia.

Thank you for your response. We will be traveling to Venice, Rome, and Naples for a week. The other week we are staying in the Tuscan region and plan on renting a car. I did a search online but I was a little confused as choices. I see there are several trains. Someone say Eurotrain? I'm originaly from NYC and and traveling by train is easy, but going to another country I know nothing about is confusing. Also, when we are in Tuscany and going to Florence I know its advised not to drive in Florence but can you park somewhere easily outside city. Thanks for any responses

Basically you have three levels of trains mostly related to speed. The most expensive will be the high speed which go primarily between the major cities. The Intercity (IC) is slower and hit more stations. The Regionale train is the slowest and hits nearly every station along the route. Think of bus on rails. All trains except the Regionales require a seat reservation that comes with the ticket when you purchase the ticket. Those trains offer some deep discount if purchased in advance on the web but locks you into in a specific schedule and change/refund restrictions on the ticket. The Regionale train is an open ticket that can be used anytime for 60 days from date of purchase and must be time stamped (validated in blue or yellow boxes on the train platform) when used. The Trenitalia.com site will list all of your train options via time. Pick the train and time that best fits your schedule. Train availability is never an issue except in some very rare circumstances.

Luckily, once you start looking into it, train travel in Italy shouldn't be too difficult to understand (I hope.) As Frank says, there are 3 different levels of the trains. If you are concerned about pricing, you may want the IC or the Regionale trains, but if you are more concerned about getting somewhere quickly, take the fast trains - called the "freccia" trains between Venice, Rome and Naples.

Start playing around with trenitalia.com to see examples of scheduling and pricing. In the top right corner there is the British flag, which is how you can change the site to English if you'd like. While schedules for the later in the summer aren't out yet, you can use fake dates to see what trains might be options. For example, when I look at the trains from Rome to Naples in early June, the regular fare is 43€ but if I want to lock into a non-refundable, non-exchangeable ticket (the super economy fare), I can go from Rome to Naples for 19€. You will find similar options on trains to Venice.

How far in advance can you buy train tickets? How far in advance are train schedules posted?

You can buy ticket when the schedule is posted which is generally around 90 days. However, two big schedule changes in June and Fall. The schedule change little from one season to another but you cannot buy until the schedule is posted. Right now, mid June is about as far out as you can go. Waiting for the summer schedule.