How do I get from Rome to Palma Campania by train in June
A wonderful starting place for these questions is the website Rome2Rio. Here's what they have to say: http://www.rome2rio.com/s/Rome/Palma-Campania
To check train schedules, use Trenitalia. Some of your travel is on regional trains, and these are only posted a week at a time, so look at a date within the next 7 days: http://www.trenitalia.com/cms/v/index.jsp?vgnextoid=4ddd1a035296f310VgnVCM1000005817f90aRCRD
These are two good resources. Bahn.com is also good for schedules. The closest train station to Palma Campania is Palma-S. Gennero. From there you'll have to do buses or taxis to Palma Campania.