Bangkok airport is currently situated at Don-muang which is around half an hour drive from the heart of Bangkok city. Flights details of Bangkok airport arrivals and departures are available with most travel agents and ticketing offices. You can also see the real time Bangkok flight schedule details including arrivals and departure at both Bangkok international airport and domestic aiport at the official web site of Airports of Thailand Public Company Limited (AOT) Check the Bangkok airport arrivals and departure timings here
Update: I think the above link is no longer giving you the latest arrival schedules at new Bangkok airport. I have found another way to provide you up to date information on new Bangkok airport arrivals.
Once you arrive at the Bangkok airport the friendly airport staff will greet you with pleasing smiles. Thailand is known as the land of smiles. You will be absolutely comfortable at the airport. One you get your baggage and come out to the Bangkok airport arrival area take a left to find services like airport Taxi and hotel bookings. You can trust these official services though they tend to be bit more expensive than the regular Bangkok taxi cabs outside the Bangkok airport.