Done it more times than I can count!
After you pick up your luggage head to the upstairs departure area. Head outside and pick up a cab that is just dropping someone off. The actual taxi area on the arrivals side is so fucked up it isn't funny, skip it.
After you get a taxi say "meter please" and if he says no get out. After you have a cab tell him "toll way" this will get you on the elevated expressway.
If you just tell him "Nana" he will get it!
120 baht for the tollway and usually 250 for the cab ride, well worth it in my opinion in order to simplify getting downtown.
Best of luck and have fun!