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.