The Trenitalia website can be terrifically helpful, or terribly confusing. The best part is that you may be able to buy tickets up to 60 days in advance and reserve spaces on Freccia (Arrow) trains using a credit card. With "Ticketless" travel, you can just board the train, find your seats, and give the conductor your booking information when he/she comes round. However, there are occasional problems when cards are accepted. If your card is rejected by the Trenitalia web site you can buy from ItaliaRail and pay in your local currency without needing to contact your credit card company: see towards the bottom of the page.
Be sure to call your credit card company just before your purchase on Trenitalia's website to let them know that you are making a foreign purchase by Internet. Otherwise your purchase may be denied. Once you select your tickets and choose your credit card option, you may be asked to sign up for another service called Verified by VISA if you want to use your VISA card. This is not much extra effort, but be prepared to respond and take note of another password that is required for this service. Multiple purchases of tickets may require multiple calls to your credit card company, as they sometimes deny the second or third purchase so you have to call again. Sometimes the customer service area will stay on the line with you to authorize each purchase as it is submitted.
Once you have purchased your "Ticketless" ticket from Trenitalia, you will receive an email confirmation at your email account. Be sure to print out a copy of your order while you are on the website--though you will get another chance when you receive your email confirmation.
Changes to reservation dates and times for Freccia trains can be made through the website at no charge--but you must have your booking code (PNR) from your e-ticket confirmation and a booking change number. For the whole process you will also need your password for your email, password for your Trenitalia account, and password for your Verified by VISA account, if applicable. Be sure to have these memorized or available to you when you are traveling in Italy in case you want to use the Internet to change reservation times/dates.
Regarding pricing, there are discounted "Economy" and "Super Economy" fares available on many trains. The rules say that these tickets may be bought until the day before travel, but the number available on each train is limited so they may sell out before then. They are available both by online booking and for purchase at train stations.
If you cannot get the web site to accept your credit card, there is no need for concern. You will still be able to purchase tickets at a train station in Italy. Trains very seldom sell out but the cheap fares do tend to sell out so booking in advance will almost always save you money - up to 80% off on some "Super Economy" fares.
Buying from ItaliaRail
From December 2010, people from outside Italy can buy Trenitalia tickets at the Trenitalia price (including the discounts for advance purchase) through www.italiarail.com. These are e-tickets, so there is no charge for delivery, and the prices in $USD, $CAD or £GBP and are very close to Trenitalia's prices in €. Buying through this site provides a way of getting the advance purchase discounts available on Trenitalia's site without paying a fee like those charged by RailEurope.....