The only practical way to get to Nang Rong, other than driving yourself, is by bus. Some Buriram-bound and most Surin-bound buses from Bangkok's Mor Chit bus terminal will stop in Nang Rong. Buses can be quite comfortable, which is important for a five hour journey. Various companies operate on the route, so you can get a bus at just about any time of day or night. I can highly recommend Sombat Tour (web site in Thai only), which has buses that leave Bangkok at 10:00 am and 9:30 pm daily.
You can also easily get to Nang Rong by bus from any of the nearby cities, such as Nakorn Ratchasima or Buriram.