Going from Brussels Airport to town is easy as 1-2-3. A train links all 3 main Brussels stations (Nord/Noord, Central/Centraal and Midi/Zuid) to the airport station located at the -1 level of the airport terminal. When you get off the plane, take the elevator or the escalator and you're there. And it's only a 20 minute train ride!
The train starts running from at around 5:30 am until past midnight. From Brussels, the first train is at around 4:40 am until 11 pm (from Bruxelles-Midi) and it will cost you 2,50 € in second class.
Some trains go further than Brussels and might take you to Ghent (and eventually Bruges) or Mons (for instance).
If you're taking the train on the weekend, check the schedule as it might be different.
For train schedule, go to http://www.b-rail.be
There is also an Express Bus Line, Line 12 starting at the Brussels Luxemburg train station, it stops at the NATO headquarter on the way to the Airport. They run (from Brussels-Luxemburg) from 7:33 am to 7:34 pm and from the airport, the buses run from 5:45 am until 11:10 pm Attention though, the buses from Brux-Lux don't run on Saturdays, Sundays and holidays BUT the one from the airport do run and stops at Schuman instead of Luxemburg.
Oh... and the ticket is 3 Euros.
Needless to say... the train seems the most efficient solution.
For more information (and alternatives) about to go or leave the airport, follow my link!