Take the Airport Shuttle to the AMTRAK Station in New Orleans. Call: +1- 504-522-3500 or visit their web site to make the reservation: www.airportshuttleneworleans.com
Cost: about 13 dollars

At the AMTRAK Station buy a ticket to Hattiesburg, MS
Check for updated departure times at www.amtrak.com or call:1800.872.7245
one train leaves at 7:27am from New Orleans to Hattiesburg . Arrives at 10:27am.
Cost: about 20 dollars

Hattiesburg Train Station (downtown)
308 Newman Street, Hattiesburg , MS 39401

http://www.hattiesburgms.com/urbandev/hct.html#maps
Fare: $0.50

http://www.downtownhattiesburg.com/HHDA_Bro_lowres.pdf
http://www.hattiesburg.org/