AirAsia flies from Bangkok to Narathiwat daily with fares starting at around 1,200B (before taxes).
Narathiwat train station is 7km out of town in the village of Tanyong, a twenty minute songtheaw ride away. If you're travelling between the regional centres, the minibuses are faster.
If you are arriving from Sungai Kolok, the bus does not necessarily take you to the centre of Narathiwat, but instead it may drop you at the post office. If this happens, just hop off near the clocktower, thus cutting out a 15 minute walk. The bus to Sungai Kolok costs 19B and takes around an hour going via Ban Taba and Tak Bai.
The mini bus from Narathiwat to Pattani costs 50B and leaves from the intersection of Wichit-Chaibun Rd and Puphapugdee Rd, just south of the Narathiwat Hotel. Minibuses to Hat Yai leave from east of the clocktower on Wichit Chaibun Rd, cost 100B and take 3 hours. A van to Yala costs 60B, Ban Taba 20B.
Narathiwat is a small place, easily walked around on foot. There are motorcycle taxis about though -- handy for a run out to the beach (15B).