Free shuttle bus from airport to go to the bus station where you can take a local bus to go downtown or around Bangkok.

Bus 552 to Khlong Toei (by Sukhumvit Road, last stop on Sukhumvit is Asoke)
Bus 552A to Bangna Paknam (Samut prakan)
Bus 553 to Srinakharin Road Paknam (Samut Prakan)
Bus 554 to Don Muang airport
Bus 555 to Central Ladphrao (department store)
Bus 555 to Don Muang (ex airport)
Bus 555 to Rangsit
Bus 556 to Southern bus terminal (bus station for people going to Kanchanaburi or to the south)
Bus 558 to Central Rama 2 (department store)
Bus 559 to Future Park Rangsit (department store)