Coming To Chiang Mai:

Transportation
Chiang mai is about 750 kilometers away from Bangkok. There are several ways of getting there:

By air
Thai Air, Nok Air and many other airlines fly regularly from Bangkok; the trip takes about 45 minutes. There are also some international flights such as Tiger Air from Singapore or Air Asia.
http://www.airasia.com/site/th/en/home.jsp

Train
There are several trains daily from Bangkok. The trip takes about 14 hours but the sleeping wagons are quite comfortable. A single trip costs around 800 baht
http://www.railway.co.th/English/index.asp or   http://www.1stopchiangmai.com/getting_here/train/

Bus
There are overnight buses which are quite comfortable. Prices differ from 600 – 900 Baht for a single trip and takes about 10 hours ride.
http://www.1stopbangkok.com/getting_here/bus/

Other good sites to check for travel from airports to train or bus stations and best ways to get around Thailand.

This is a good site of how to take train in Thailand http://www.seat61.com/Thailand.htm

Airport Express AE4 from Suvarnabhumi International Airport to Hua Lumpong Railway Station the is cost 150 Baht one way.          http://www.bangkokairportonline.com/node/55