Matera  is the capital of the Matera province in the Basilicata region of Italy. It boasts the sassi, well-preserved rock-cut settlements that are a World Heritage site and one of Southern Italy's many important attractions.
Matera is a fairly big city. One of its quarters is the old city. Just outside the old city are the Sassi - cave houses dug into the limestone rocks. The sassi are located on both sides of a valley. On the north side the Sasso Barisano have been partially commercially developed as offices and housing. The Sasso Caveoso, on the south side, is the most historically interesting.
Matera is most easily reached from Bari in the Apulia region. The Ferrovie Appulo Lucane (FAL) runs trains from Bari to Matera Centrale, taking 1h30min with departures every 1-2 hours during the daytime. The FAL train station in Bari is located just outside of Bari Centrale and is toward the left as you walk out onto the large piazza with the buses and fountain. The company website is now up to date. The FAL does not run trains on Sunday, and does not accept rail passes. Tickets are €4.90 each way and can be purchased from the ticket machines. The platform is at a higher level so when you enter, turn right and take the elevator to the 1st floor.
After exiting Matera Centrale, there is a piazza to the left with various buses. From here, "Linea Sassi" buses to I Sassi di Matera every 30 minutes; the inexpensive tickets are sold upon boarding. The Sassi can also be reached on foot in about 20 minutes by walking straight ahead downhill from the piazza. The Sassi themselves can only be explored on foot, and tourist information is available locally.
It is highly recommended the use of a local tour guide, to really make some sense of various aspects of the old city, which is indeed one of a kind in its genre. To get in contact with a local guide without paying agencies, try with www.materatourguide.it .This is one of the top listed guides recommended by travellers, if you go to visit Matera.
The Women's Fiction Festival is held late every September in the Sassi District, and attracts an international contingent of writers, agents and editors. 
Go hiking across the river to see caves and old churches embedded in the rock. Start from the carpark on via Madonna delle Virtu. To cross the river you can try jumping from rock to rock if you are nimble or utilise the temporary bridges if you are not. You can visit the old city with Ape tour in Matera Ape nei Sassi.
There are many restaurants in the old city as well as outside.
If you hire a tour guide, make sure they are licensed. Many people might stop you to offer tourist services that are only looking to take your money.