There are two airports in Brussels. If you come from Zaventem airport (the national airport of Belgium), you can catch a train to Maastricht. Follow the escalators all the way down to floor -1, which is the train station. Here, you can buy a ticket for €13,90. The fastest way back to Maastricht from the airport is to take the train from Brussels Airport -> Leuven, Leuven -> Liege Guillemins and finally Liege -> Maastricht.
Be aware- the train station is called “Brussels Airport Zaventem”. Don’t book your ticket for just “Zaventem”, as this is the town next to the airport and not the airport itself.
If you fly to Brussels South Charleroi Airport then you can also get the train to Liege (Guillemins) and then to Maastricht. You will have to take the shuttle bus A from Charleroi airport to Charleroi train station first though. This shuttle bus costs €5.
If you are travelling from Belgium to Maastricht, you should definitely check out the Go Pass 1 Maastricht! This is a special ticket which allows you to travel between Maastricht and any station in Belgium for only €8,50. However, be aware that you may have to pay a bit extra in order to get to the airport stations. You can order you Go Pass online here.