According to some sources I found:
- You need to request a permit from your city and your canton's water and sewage department
- To get a permit, you need a "proof of utility", so you can't just dig a well for fun, it needs to bring some benefit.
- You need a written technical planning document as well, including an analysis on the energy- and cost-efficiency of your project
- If you want to drill down to the groundwater (for drinking water quality), you need additional analyses being done, to prove that the project conforms to standards and causes no harm.
It sure sounds fun to have your own well, but I think I'll stick to collecting rain water.