There are three main airports in the Netherlands.
Maastricht/Aachen airport is the closest airport. The only way of getting to and from this airport by public transport is by taking bus number 59. It goes from the airport to Maastricht’s central station and leaves every half hour. The journey takes half an hour and should cost under €5.
Coming from Amsterdam airport you need to get a ticket from Amsterdam/Schipol Airport to Maastricht Central Station. This costs around €25 and takes around two and a half hours. You have to change trains either in Utrecht Central or Sittard.
Eindhoven airport presents another excellent airport to use for travelling to Maastricht. To get from Eindhoven to Maastricht, simply catch the 400 or 401 bus from the airport bus station to Eindhoven central train station. This takes approximately 30 minutes and buses leave every half hour. From here you can catch a train to Maastricht which takes 1 hour. The overall journey price is around €19.
All of the prices mentioned are the current standard prices when using an OV chipkaart without a discount.