The best way from the Brussels airport to Maastricht is by rail.
The German Rail website is very easy to use and has an English language option. It is useful for all of Europe and not just Germany. It is
www.bahn.de .
I'm guessing from the US that you'll arrive on a Sunday. So, using Sunday July 29
as a search date and 08:00 as a time you get:
Leave Brussels Airport rail station at 08:46
Arrive Brussels Nord station at 9:01
Leave Brussels Nord at 9:06
Arrive Liege-Guillemins at 10:02
Leave Liege-Guillemins at 10:18
Arrive Maastricht at 10:46
Additional trains leave the airport at 9:46, 10:46, 11:46 and so on and follow the same schedule of intermediate times.
It is quicker and easier to get to Maastricht from Brussels than from Amsterdam.
Trains run from the airport very often. Google "Brussels airport" to get information on where the station is and how often the trains run. Note that the Brussels RLD is next to the Nord station, so if you arrive early you can check it out.