You can visit one of the many bike shops to buy a new or second hand bicycle. it is also quite easy to pick up a second hand bike through Facebook. Buy/Sell a bike in Maastricht is a good place to start, but you will find a number of similar pages with a quick search. Since you’re dealing with second hand bikes from a person you don’t know, you’re buying the bike in good faith and it could be stolen. Ask the seller to write and sign a document stating he is the rightful owner of the bike, the serial number of the bike, the date, location and price you bought the bike for. This way you cover yourself for any legal liability in the event you bought a stolen bike in good faith. Other options are Marktplaats or Zuydfiets. Often you can also sell your bike here as well. Always go and see the bike before you decide to buy it. That way you can check if the bike is in good shape and you can write down the seller’s contact details just in case something goes wrong.
If you’re on a limited budget but are willing to do a little work in exchange for a bike, try the Fietsbank Maastricht. This is a foundation by volunteers who dedicate themselves to making bikes and bike repairs available for people on a limited income. You can also donate bikes and spare parts.