The simplest way to get to Buriram is by bus. Buses leave Bangkok's Mor Chit bus station regularly for the roughly five hour trip. The fare from Bangkok is around 300 Baht (7.79 USD). You can also easily get to Buriram by bus from any of the neighboring provices.
Buriram does have a rather new airport, so it is possible to fly there. However, as of January 2010, low-cost carrier Nok Air was the only airline flying to Buriram, with twice-weekly flights.
You can also reach Buriram by train. There are six to seven trains a day from Bangkok's Hualumpong station. All trains bound for Ubon Ratchathani stop in Buriram.