...is easier now. Freccia train from Napoli Centrale to Salerno (less than 40 minutes), then change to the FrecciaLink minibus that leaves from the piazza in front of the train station. This is a new service that doesn't appear on the Arrivi/Partenze posters, but you can buy tickets online or at the station in Napoli. This ride must be part of your Napoli-Matera or Matera-Napoli ticket, you cannot just buy it from the bus driver. Only two FrecciaLink departures daily at this writing.
Italo also has a minibus for this route.
EDIT: no option to buy a Matera-Salerno or vice versa, only Matera-Napoli or Napoli-Matera.