Don Mueang Airport was the main Bangkok Airport. Currently Suvarnabhumi Airport is the main airport, but there are still many flights fly from and to Don Mueang Airport especially flights from low cost airlines such as Air Asia, Nok Air, and so on.
Don Mueang Airport is located in Bangkok and is not far from the city center, but it does not connect with any rapid transit system (BTS Skytrain and MRT Subway). The closet BTS Station to Don Mueang Airport is Mo Chit Station and the closet MRT Station to Don Mueang Airport is Chatuchak Park Station. These two stations are located in the same area, Mo Chit.
Then, from these stations, you can take bus or taxi to the airport. Taxi might be the easiest option. If you travel during peak hours, tell the drivers to take the tollway. But if you want to save money, I recommend you to take the special bus number ‘A1’. This bus runs between Mo Chit and the airport from 07.30 to 23.30. It takes the tollway and the fare costs 30 baht throughout the route.