Hello Jacquelyn and welcome to our community. There aren't any direct trains from Rome to Praiano. You could take the train20 from Rome to Naples (Napoli Centrale). From there, you could take the Circumvesuviana Campania Express24 train to Sorrento. And then from there, the SITA bus to Praiano158. In all three cases, you can buy the tickets in the stations. You could pre-purchase the Rome-Naples ticket on ItaliaRail20 in advance.
Alternatively, you could look into renting a car or a private driver service.
Hope this helps! Let us know if you have any other questions.