What discolored water actually means
Discolored water looks scary and is almost never dangerous. In most homes it's rust or mineral sediment that got stirred up, either in your own pipes or in the city main.
The color tells you a lot. Brown, orange, or yellow means iron (rust). Black or dark specks usually mean manganese. Milky white means dissolved air, which is completely harmless.
Your first move is free: run the cold tap for 5 to 10 minutes. A huge share of these calls clear up right there, and you save yourself a service fee.
The next question is where it's coming from. If only the hot water is off-color, your supply line is fine and the water heater is the culprit. If both are brown, look at the pipes or the utility.
The usual suspects, ranked
Most discolored-water cases fall into a handful of buckets, and you can narrow yours down in about ten minutes.
Neighborhood-wide brown water that shows up suddenly is almost always the utility flushing hydrants or a nearby main break. It clears on its own. This isn't your problem to fix and it isn't your plumber's either.
House-only brown water that comes back every morning points at corroding galvanized pipe. Homes built before about 1970 are the prime candidates, and once the rust starts shedding it doesn't stop.
Discoloration on the hot side only is the water heater, full stop. Sediment builds on the tank floor and breaks loose when the burner fires. A flush often buys you years.
On a well, iron and manganese are baked into the groundwater in a lot of regions. That's a treatment problem, not a plumbing leak, and it needs testing to fix right.