There is a wet patch and you cannot find where it is coming from.

Close the main shut-off valve, wait fifteen minutes with nothing running, and look at the water meter. If it is still turning, you have a leak on a pressurized supply line. If it has stopped completely, the water is coming from a drain, a roof, an appliance, the ground, or condensation, and the whole search changes.

That is one test, it takes a quarter of an hour, and it eliminates half the possibilities. Do it before you start cutting anything open.

Water does not appear where it leaks

This is the single fact that makes these hard, and it is true in every building. Water enters at one point, travels along whatever surface it lands on, and emerges at the first low point or the first seam it reaches. That path can be several feet, and it can run in a direction that makes no sense from where you are standing.

So the wet patch is a symptom, and its location is evidence, not an answer.

On a ceiling, it is almost never directly under the leak. Water runs along the top of the drywall and along joists until it finds a seam, a light fixture, or a nail head.
On a floor, it emerges at the edges of a room and at seams in the flooring, because that is where the path out of a subfloor is.
On a wall, it shows at the baseboard, which may be a long way below and to the side of where it entered.

Narrow it by when it happens

The timing tells you more than the location does. Watch for a day and write down what was running.

Constant, no matter what you do: a supply line under pressure. This is what the meter test detects, and it is the most urgent kind, because it does not stop on its own.

Only when a fixture drains, a shower, a sink, a washing machine discharge, a toilet flush: a drain or waste leak. Drains are not under pressure, so they only leak while something is going down them. This is why a shower can leak for years and only ever be wet after someone showers.

Only after rain: a roof, a window, a wall penetration, or ground water. Correlate it with the weather rather than with the plumbing. Rain and ground water are treated differently by insurers, so knowing which it is matters beyond the repair.

Only in cold weather, and worst on cold nights: condensation, or an ice dam. Warm humid indoor air meets a cold surface, usually in an attic, a crawl space, on a cold water pipe, or on ductwork, and water forms on it. It looks exactly like a leak and there is no leak.

Only when the heating or the air conditioning runs: the condensate line from an air conditioner or a high efficiency furnace, which blocks with algae and overflows its pan. This is one of the most common summer wet ceilings.

Once, and never again: an overflow. A bath, a sink, a pet bowl, a spill somebody did not mention.

Then look in the places these actually start

Working from the most common down:

Toilet. The wax ring at the base is a classic slow leak that shows up in the ceiling below or at the flooring around the base. Rock the bowl gently: if it moves, suspect it.
Shower or tub. Failed grout or sealant at the base, a leaking drain connection, or a shower pan that has split. Test by filling the tub and letting it stand, then separately by running the shower, and see which one produces water.
Under sinks. Look at the trap, the supply connections, and the back of the cabinet, not just the floor of it. Run a hand along the underside of every pipe. Feel, do not look, because a slow leak leaves nothing to see.
Dishwasher and washing machine. Both leak underneath and behind, where you cannot see them. How to check them, and what to close first.
Water heater. A slow weep from a fitting or a relief valve. What the leak location on a heater tells you.
Air conditioner condensate pan and line, in the attic or at the air handler.
Refrigerator ice maker line, which usually leaks behind the fridge or in the ceiling below.
Windows and door thresholds, if it correlates with rain.
The roof, remembering that most roof leaks are at flashing, and that the entry point is uphill of the stain. What to do while it is happening.

Simple tests that cost nothing

The meter test, described above. Rerun it with individual fixture valves closed to isolate which branch.
Dry it and mark it. Dry the patch completely, then draw around the edge in pencil and put the date on it. If it comes back, and how far past the line it goes, tells you the rate.
Paper towel. Lay dry paper towel along suspect pipes and under fittings. It finds a weep your eye will not.
Food coloring in the toilet tank. If color appears in the bowl without flushing, the flapper is leaking, which explains meter movement and a bill but not usually a wet floor.
Tissue at the base of a toilet or a shower, checked after use.
Run one thing at a time. Shower only, then tub only, then washing machine only, waiting between each. Tedious, and it is how these get found.
Look in the attic or crawl space with a flashlight, following the dry water track. Old tracks are stained; a live one is wet.

When to stop looking and call someone

Call a plumber when the meter says there is a supply leak and you cannot find it, because that water is going somewhere structural right now. A leak detection specialist has acoustic equipment, thermal cameras, and pressure test kit that finds in an hour what you will not find in a weekend.

Call a restoration company rather than a plumber when the source has stopped but the wet area is large, has been wet for a while, or is inside a floor or a wall cavity. The distinction between the two trades is what water is doing right now.

Do not wait to see if it goes away

The reason to chase this now rather than next month is not the water. It is that the mold window is 24 to 48 hours from when material gets wet, and a slow hidden leak has usually been running well past that before anyone notices it.

It matters for the claim as well. Most policies cover sudden and accidental water damage and exclude damage that happened gradually. A leak found and reported when you first notice it is a different conversation from one you watched for six months. The gradual damage exclusion is the most common reason these claims are denied, so document the date you first saw it.

The short version

Meter test first: still moving means a pressurized supply leak, stopped means look elsewhere. Use when it appears rather than where. Water emerges downhill and sideways of where it enters. Mark and date the patch. Chase it now, because both the drying window and the insurance argument run from when it started.