Don Mueang Airport (DMK) was the main Bangkok airport. Nowadays even if it is not the main airport, there are still many flights fly from and to Don Mueang Airport. It is a hub for low cost airlines such as AirAsia, Nok Air, Thai Lion Air, and so on.
Unlike Suvarnabhumi Airport, Don Mueang Airport does not have a connection with an express rail. However, there are several transportation modes you can take to Bangkok city center.
Both normal and air-Conditioned buses are available. The train is located just 500 meters away from the airport. And of course, taxis are waiting to take you to anywhere at the airport. Besides, you can rent a car at the airport. You can see more detail here.
In case that you want to save money and are not familiar with Bangkok and the bus here, I recommend you to take the special bus ‘A1’ that runs between the airport and BTS Sky train-Mochit Station/ MRT Subway-Chatuchak Station. The ‘A1’ bus runs from 07.30 to 23.30, and the fare costs 30 baht throughout the route. The bus takes the tollway, so it does not take much time to reach BTS and MRT. Then, you can take the BTS or MRT to the city center.
Hope the information helps