There are trains from Naples that head in the direction of Contursi, that get close enough for a pick up from Battipaglia (30 min drive away), but don't get the full way.
You will either need to get a cab (expensive) or the
Alibus (around €5) from Naples Airport to Napoli Centrale Station in Piazza Garibaldi. The Alibus pickup stop is a 5 minute walk from the airport and should be signposted - you can buy your ticket with Apple Pay/Contactless when boarding.
From there you can get a train to Battipaglia (you may have to change at Salerno, but there are also direct ones available).
The best option to book tickets and check timetables is via the Trenitalia app, although Trainline does also offer Italian train tickets.
From Battipaglia it's a 30 minute drive to Contursi - there is
some taxi availability in Battipaglia, although it likely cheaper & easier to arrange a pickup from your hotel.
If the Battipaglia connection is problematic, let us know and we can look to get a friend/family member to come collect you.