You turned on the water: Nothing!
With extremely cold weather or a long period of pretty cold weather, you're likely to come up with frozen pipes, on hot or cold water taps. It could happen in the bathroom and not in the kitchen, or vice versa. Or worse, both.
Water will freeze if the pipes run up an uninsulated wall, in an unheated crawl space or attic, or even in the basement, particularly near the concrete or stone foundation. It can happen even if the house is heated normally, and is more likely if heat is lost.
When water freezes, it expands in volume about 8 percent, which can burst pipes. If the freeze is in a straight run, the pipes may not burst because there is room for the ice to expand. Bursting is most likely to occur when the freeze is at a corner or junction.
So, when you unfreeze a pipe, you have to be alert to immediate leaks. In that case, turn off the water and call a plumber, unless you're handy enough to make your own repairs.
How to unfreeze a pipe: Turn on the faucet and leave it on. If the pipe is accessible, apply heat, working from the faucet toward the source of water. If you melt ice in the middle of a freeze, you could create steam, which could cause an explosion or at least a serious breakage.
The fastest source of heat is a propane torch, with a flame spreader. Use a fireproof material behind the pipe, and be careful not to overheat the pipe. As you work, you may see water trickling from the faucet. If this happens, move a little way down the pipe. The flame torch is the only thing you can use in case of a power failure.
If you have power, you can use an electric putty torch, an electric hair dryer, or the blower attachment to a vacuum cleaner. Put the hair dryer on "high." This is slower than a flame torch, but safer.
A heating pad can be wrapped and tied around the pipe. A horizontal pipe can be wrapped and tied with towels and boiling water poured in a light but steady steam over them.
Wrap an electric heating tape around the pipe and plug it in. Secure it with tape so it will stay put.
If the pipes are inaccessible, set a heat lamp at least six inches away from the wall containing the pipe. Avoid scorching or blistering paint or paper. Position the lamp with rubber-ended clamps, attached to a stepladder or other device. Move it when necessary.
How to keep pipes from freezing: There is not much you can do with pipes in an uninsulated wall except to insulate the wall. If the wall is already insulated, you may have to open it up and make sure the insulation is on the outside of the pipe.
For pipes under a sink cabinet, keep the cabinet door open so house heat can warm the area.
For accessible pipes, pipe insulation is good. There are many kinds, including slit tubes that are slipped over the pipe, and strips of insulation wrapped spiral fashion around the pipe.
Electric heating tapes, installed under insulation, are often thermostatically controlled to go on only when temperatures get below a certain point.
Hang a trouble light (use a 100-wat bulb) on the affected pipe. This is useful when pipes are near a cold foundation.
An old but good techniques is to keep the faucet on at a trickle. A drip won't do; it has to be a trickle.