First you must purchase a ticket to Bangkok, Thailand. Kayak is a great place to do this.
Flying to Surat Thani from Bangkok:
Surat Thani airport is served by THAI and Thai AirAsia, with the later having more affordable rates (starting at 800B, but watch out for the plethora of “fees” that get added to this base rate). The flight from Bangkok to Surat Thani takes 70 minutes. Surat Thani airport is around 30km north of Surat Thani town, so you’ll need to transfer into Surat Thani ( Inquire about bus transport,Taxi is a ripoff ) and then arrange onwards bus and boat connections to the island of KoaPhangan. Full fare and timetable information is available on the AirAsia website.
Alternately you can take a overnight a/c sleeper train for 600-700Thb. These trains are clean, comfortable, and quick. You can book online at www.thairailticket.com
Bus is 1.5 hrs, ferry about 2 hrs. It is a pleasant trip.
Ferry to Koh Phangan time table here