... by plane: Bari-Palese airport is the nearest to Matera.
You need to take a taxi or to rent a car in Palese to go to Matera.
If you take a car, you can go through the road S.S. 96 towards Altamura and then continue to Matera.
...by auto: From Napoli, you can go on the motorway towards Salerno, then follow the motorway A3 in the direction of Reggio Calabria. At Sicignano you have to continue to Potenza, where you have to take the road S.S. 407 (Basentana) until the junction for Matera near Ferrandina Scalo. Continue to Matera.
From Bari, you can follow the road S.S. 96 towards Altamura and then continue to Matera.
From Calabria, on the road S.S. 106 (Ionica), coasting Ionio Sea, near Metaponto, there is a junction for the road S.S. 175 for Matera. Junction Matera Centro.
...by train: From Roma and Napoli there are trains to Ferrandina. In Ferrandina there are connections to Matera by bus.
From Bari there are Ferrovie Appulo-Lucane (FAL) with a lof of trains and buses to Matera.