From Guiyang airport, you can take a mini-van walk to the right from the airport exit till you reach the mini-van station. However, the vans depart when filled, which may cause waits. 60yuan one way as of December 2010.
There are busses from provincial capital Guiyang, a few hours away to the West. You can also reach Kaili by going North and West from Guilin in neighboring Guangxi, by bus via Sanjiang and Congjiang.
Kaili is on a railroad line connecting Kunming and Changsha. You could get a train from either of those, or from Guiyang.