The International Airport of Brussels at Zaventem (North of Brussels).

The most convenient way to travel from this airport is by train. The train station is located in the airport terminal itself. You rail with the Airport Express to one (of the 3) train stations of Brussels (runs every 20 min). In one of these stations (it does not matter which one), you switch to the regular train to Bruges (runs every 30 min). 
To verify the train timetables and buy tickets online visit the official website of the Belgian Railway Company

Once you arrive at the train station of Bruges, follow the directions: When you arrive at the train station.

The airport of Brussels South at Charleroi.

Although you also can take the train here it is more complicated and takes longer. To plan your trip from this airport to Bruges by train, please use the official website of the Belgian Railway Company.

You also can rent a car at the airport. For driving directions once you arrive in Bruges, follow these directions: When you come by car.

There is also a shuttle service with bus from Charleroi airport to Bruges train station. The shuttle bus is operated by FLIBCO and has 9 departures per day. For details and reservations, please visit the website of FLIBCO.

Once you arrive at the train station of Bruges, follow the directions: When you arrive at the train station.