Unfortunately there are currently no links from Suvarnabhumi to central Bangkok by train, or by the popular skytrain and metro systems. The "Suvarnabhumi Airport Link" rail system which will take passengers from Suvarnabhumi to Makkasan in central Bangkok, and provide connections to both the Skytrain and Metro, is under construction and is scheduled for completion in 2007. Media reports have cast doubt on whether this is a realistic deadline however, so it may well be 2008 before it's fully operational. There are also plans to extend the Skytrain line from On Nut to Suvarnabhumi, but the timeline for this is unclear.
By Bus
Suvarnabhumi has a dedicated bus terminal at it's Transportation Center with plenty of services both within Bangkok and to provinces in Thailand's north-eastern and eastern regions.
Within Bangkok
The local buses to downtown Bangkok cost a flat fare of 35B a person, so they're certainly cheap if somewhat slow and crowded The Airports Authority of Thailand advertises the following public bus routes as being available from Suvarnabhumi:.
Bus no. 549 Bang Kapi - Minburi - Suvarnabhumi
Bus no. 550 Happyland - Suvarnabhumi
Bus no. 551 Victory Monument - Suvarnabhumi (via Pratunam)
Bus no. 554 Rangsit - Suvarnabhumi
Bus no. 552 Onnut Skytrain Station - Suvarnabhumi
Bus no. 553 Samut Prakan - Suvarnabhumi
Of these the most useful to tourists looks like being the route 552 with it's connection to On Nut skytrain station.
Out of Bangkok
Thailand's Transport Company has quite a few public buses leaving from the bus terminal at Suvarnabhumi which cover most of the major destinations in Thailand's eastern and north-eastern regions. 3 of them, routes 389, 390 and 825, are new routes from Suvarnabhumi while the others are existing services that leave throughout the day from Mo Chit and Ekamai bus stations and stop at Suvarnabhumi en-route.
Many of these routes are very useful to tourists. The most popular are routes 9905 and 389 going to Pattaya, 9906 for Ko Samet (Rayong), 9908 for Ko Chang (Trat) and route 825 for it's connections to most of North-Eastern Thailands largest cities
Route 55: Ekamai - Suvarnabhumi airport - Chachoengsao province
Route 390: Suvarnabhumi airport - Aranyaprathet (Sa Kaew province, on the Cambodian border) Departures at 08.00 , 11.00
Route 825: Suvarnabhumi airport - Saraburi - Nakhon Ratchasima - Khon Kaen - Udon Thani - Nong Khai (on the border with Vientiane in Laos) Departures at 06.00 , 22.30
Limousine
This is booked from a taxi booth inside the terminal when you're leaving arrivals - their representatives may try and
lead you here claiming it is the public taxi stand. 'Limousine'
is a flattering description, these are really just somewhat newer and more
comfortable taxis. Costs vary from 600B or so up to 1500B depending on your destination downtown. There are only two official limousine services allowed to operate with the terminal, though of course any private company can arrange to pick up at arrivals too.