There are two main airports in Germany that are easy to get to from Maastricht.
If you are travelling from Düsseldorf International airport in Germany, you first get the sky train from the terminal to the Düsseldorf airport train station. From here you can get a one way ticket to Maastricht for around €20. Journey times can vary but the average time is about 2.5 hours.
When Travelling from Cologne (“Köln”)/Bonn airport, you first have to catch the shuttle bus from terminal 1 to the Cologne Central train station. This costs around €4.80. From Cologne main station you can then take either a bus or a train to Aachen for around €20. This takes around one and a half hours. From Aachen you can catch Arriva Qliner 350 which takes you to Maastricht central station.