Found this...
"The journey downtown will take from between 30 minutes to 2 hours depending on the traffic and where you're going. The closest popular tourist area to the airport is the Sukhumvit road district, which on a good day will take around 30-45 minutes to get too. Silom, Sathorn, and Siam Square will take about 45 minutes to an hour to reach while if you're heading over to Khao San road it could well take over an hour. Heavy traffic can make this journey a lot longer though, and so you have the option of using the expressway downtown for an additional charge of 25B to pay. This is paid for by the passenger, though the driver may pay at the time and you'll be expected to pay at the end. The expressway is substantially faster at any time during the day, though if you're arriving late at night it's not usually necessary to go on the expressway as the traffic is light on the main roads.
The passenger also has to pay a 50B airport surcharge on top of the metered fee. Just like at the previous Don Muang airport, it's possible (though officially prohibited) to get a taxi from the departures area which has just dropped off passengers instead and save the 50B surcharge and the queues. This avoids the official safeguards too though, and so if you're not experienced with Bangkok yet it's best to stick to the official channels. Unlike at Don Muang though, this airport is somewhat in the middle of nowhere so it's no longer possible to walk to the main road and hail a taxi from there.
With all the fees included, the total cost will be around 250B for Sukhumvit up to 350B - 400B to Khao San.
Try and get some change at the airport of 1000B notes to 20B, 50B and 100B ones, don't be surprised if the taxi driver hasn't got (or claims not to have) any change. If you do get caught in this kind of situation, you can always get out and get smaller notes by buying something from the nearest 7-11 store. This tactic often leads to the driver suddenly remembering where his change is kept."
Pretty much sums up what you want to know or?
Btw. Here is all the info..
Taking a taxi