Symptoms
Well water problems, by what you can see
Most people meet their water chemistry through a stain or a smell rather than a lab report. Each page here works back from the symptom to the short list of causes, and says which test would settle it.
Black stains or black specks in well water
Manganese, in most cases, and it turns up at a twentieth of the concentration iron needs to cause trouble. It is also the reason a new iron filter sometimes fixes the orange staining and leaves the black staining exactly as it was.
Blue-green stains in sinks and tubs
Copper, dissolved out of your own plumbing by acidic water and redeposited where water sits. The water arrived at the house without it.
Cloudy or milky well water
Three possible causes, and a glass of water separates them. Cloudiness that clears from the bottom upward is dissolved air and needs nothing. Particles that settle are sediment. A haze that does not clear, especially with an orange tint, is precipitated iron.
Orange or rust stains from well water
Iron, in essentially every case. The useful question is not whether it is iron but which form, because dissolved iron and already-oxidised iron need different equipment.
Slime or sludge in well water
Iron bacteria, most likely. They are living organisms that metabolise iron and produce a slime as they go, and that slime is why this problem does not respond to the equipment that handles ordinary iron.
Well water smells like rotten eggs
Hydrogen sulfide. Run the hot and cold taps separately before doing anything else, because if only the hot water smells, the water heater is manufacturing it and the repair costs a fraction of a treatment system.