Both Wille and Rutger told me that the kommun would test our well water. I took a sample last week, and it was pretty yellow when I bottled it, although it still tasted and smelled fine. One reason for testing is to see if a filter is recommended, and if so, what kind of filter. Janne says there are many types, and installing one is no problem.
I just sent an email, all in Swedish, to Värmdö kommun to inquire about testing. Let's see if I have any luck with my inquiry!
UPDATE: After reading Marg's comments, I decided to take a different tack and have ordered this kit. My goal is to have a general sense of our water so we can decide if we want a filter, and if so, what kind. I hope this kit will do the trick; if not, it wasn't that expensive.