By Plane

The nearest airport is Bari-Palese www.aeroportidipuglia.it, which is about 60km far from Matera.
Once you land you can reach Matera by:
Shuttle bus: www.cotrab.it
Train: FAL from Bari Central Station to Matera, ferrovieappulolucane.it[on public holidays there are only few FAL buses, not trains]

How to reach Bari Central Station from the airport:
Train: Ferrotramviaria s.p.a. www.ferrovienordbarese.it
Urban service Bus No. 16  www.amtab.it
Shuttle bus airport- central station  www.autoservizitempesta.it
Other airports are those of Brindisi www.aeroportidipuglia.it/homepagebrindisi
and Naples www.aeroportodinapoli.it

By train

From Bari
If you arrive in Bari with “Trenitalia”, exit from the Bari Central Station and then turn left to reach FAL: ferrovieappulolucane.it [On public holidays there are only few FAL buses, not trains.]

By bus

There are several companies connecting Matera with main Italian cities:
Marozzi www.marozzivt.it and Liscio www.autolineeliscio.it connect Matera with Rome, Florence, Pisa and Siena
Marino www.marinobus.it connects Matera with Milan, Ancona, Bologna and Naples
Petruzzi www.petruzziautolinee.it connects Matera with Bologna, Modena, Parma, Chieti, Pescara, Rimini
Miccolis www.prenotazioni-miccolis-spa.it connects Matera with Lecce, Brindisi, Salerno, Napoli
Flixbus www.flixbus.it connects Matera with several destinations.

By car

From Northern Italy: highway A14 up to Bari Nord exit and then follow indication for Altamura – Matera street.
From Rome-Naples: highway A3 Salerno-Reggio Calabria. Exit Sicignano degli Alburni -Potenza, take the SS407 towards Metaponto. Then take SS7 “Appia” for Matera.