You can find trains in Italy on the site of the Italian railway site:
http://www.trenitalia.com/cms/v/index.jsp?vgnextoid=ee13721bdd69a110VgnVCM1000003f16f90aRCRD
In it you can enter your departure station, your arrival station and adjust the date and time you want to travel.
You can buy tickets for the next three months (some exceptions are possible) and in December the timetable will likely change, but mostly the changes are not too big.
Most trains will have first class but if you have a reserved seat you will likely find the basic services (2nd class) good enough. First class is mostly much more expensive but sometimes it is not much more expensive or even cheaper in some rare cases.
So it is worth checking out before buying the tickets.
There are so many rail services that it is hard to give you a short overview.