I need to get from the Cinque Terre to Rome in August. When/where can I buy train tickets? Also, how much are they? And is the ride scenic? I have been to the trenitalia website, but couldn't get any prices.

The tickets on an IC+ and IC will cost about 43 Euros for 1st class and 32 Euros for 2nd class. That's from Monterosso to Rome; you didn't say where you'd be starting from in CT. The ride is fairly scenic, you'll pass the Carrara marble quarries and it will look like snow on the mountains.

If you go to trenitalia, don't put in the dates you want to travel. Put in a date about 3 weeks out from today. When it shows you your options, click on the shopping cart on the right to see the prices. You can't buy tickets or see the prices if your requested dates are more than 60 days out.
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Thanks for the tip! What is the difference between first and second class? Does first mean a compartment by yourself?

No, but the seats are roomier in 1st class.

Have you heard of last minute deals on Trenitalia? These are deals that you can only book one week in advance (it's called Happy Trains). A lot of fares are only 10Euros!!! The catch is that you cannot change the itinerary afterwards. But, for 10E, you can't ask for more.