Paestum is fairly far from Naples, but by train you can reach it in an hour. Maybe stop off at Salerno and take a walk around the seaside town. Paestum train station is unmanned and getting from the station to the site is easy. Exit the station and foloow the road in front of the station and walk away from the station and towards the medieval city walls. Walk under the old city gates and follow the dusty path for a few minutes until you reach the end. To the left is the entrance to the Paestum site and museum, to the right are stores and restaurants. It's best to bring lots of water and maybe umbrella or hat to avoid the sun because there is little shade there. When you leave, make sure you get on the platform thats next to the station building if you want to go back to Naples. The train tracks there only goes north or south, so make sure you remember which way you need to go. Also the station messages are all in Italian. Paestum is far off the tourist trail but its a great and peaceful place to visit, with 3 Greek doric temples to see and also a Roman town too. The best preserved temple is the temple of Athena. There is even a Roman bath house too there.
