Water forget-me-not is semi-aquatic and usually grows in ponds and swamps, because it likes very moist soil. It can even grow in water if it's not too deep (<10 cm).
Sadly, I don't have a pond, so I'm trying to grow it on my balcony in a pot. Is there anything I need to do besides keeping the soil wet all the time?
I decided to answer this question myself, because I have this plant for already several months, and it's doing well.
It turned out that water forget-me-not doesn't really need to grow in water. I've been keeping it in a clay pot and watering it regularly to keep the soil moist, so basically just treating it like any other plant that likes water. So far it looks green and happy, grows fast and doesn't require any special treatment.