Hi Joran and welcome!
You are right, broken screws are a common problem. However, to solve it you have to differentiate between two conditions:
1. The screw bolt looks out of the hole and is long enough:
Try to grab the remaining bolt by using nippers or put two nuts on it and tighten them mutually, unscrew the bolt.
2. If there is no bolt looking out or it's too short:
You'll need a screw extractor set like this one (
click me). It's a bit tricky to drill the hole in the bolt which is necessary to use the screw extractors. May be you should ask a mechanic for help.
I hope so, this small instruction will help you. Please feel free to ask if there are some questions left.
To success!