Stop the water first
Shut off the main. It's usually where the water line comes into the house — in a crawl space, a garage, near the water heater, or low on an outside wall. Turn it clockwise until it stops.
If the break is before that valve, or the valve won't move, the next shut-off is at the meter by the street. The meter and the street-side valve belong to your water district, not to you or the City of Burien. Burien is served by five water providers — Highline Water District, King County Water District 20, Water District 49, Water District 125 and Seattle Public Utilities — and the city's utilities page has a map of which serves your address. Call the district for your address; they can shut it off.
Once the water is off, open a tap at the lowest point in the house to drain what's left in the pipes. If water has reached outlets or the panel, keep out of that room.
Q1I can see it leaking through the wall right now. Should I open the wall?
Shut off the water first. Then, if the drywall is bulging, a small hole at the lowest point with a bucket under it lets the water out in a controlled way rather than all at once. Don't cut further than that — opening the wall properly is part of drying it, and it's easier to do once someone can see where the pipes run.
Q2It's only a small spray from a copper line. Can it wait until morning?
Only if the water is off. A small spray under a sink or in a wall puts out more water overnight than most people expect, and pinhole leaks can open up. Shut off the main, or the valve for that fixture if there is one, and it can wait for a plumber. The wet cabinet or wall still needs drying either way.
Q3The water meter is running with everything turned off. Is that a leak?
Almost certainly. If every tap, toilet and appliance is off and the meter is still moving, water is going somewhere — often a pipe under the house, in a wall or in the ground between the meter and the house. Keep the main off where you can, and get it traced before the damage shows.
Q4There was water coming out of the ground near the house. Whose problem is that?
It depends which side of the meter it's on. The line from the meter to the house is usually the owner's; the meter and the street side belong to the water district. If it's between the meter and the house, it's a plumber for the pipe. If it's reached the foundation or the crawl space, that's where the water damage is.