Temperatures this brutally cold can cause water pipes to freeze, particularly pipes that lead to outdoor spigots or pipes in unheated spaces.
Pay particular attention to pipes on outside walls. Open the doors of under-sink cabinets to allow warm air inside, and turn faucets on just enough to produce a trickle of hot and cold water overnight. And just for these frigid nights, it's a good idea not to turn the thermostat back at night as you usually do. The extra money you'll pay for water and heat is far less than the cost of a plumbing repair.
Disconnect hoses from outdoor spigots so the freezing water in the hoses doesn't damage the plumbing when it expands. Turn on the spigots, and then go inside and shut off the water supply to them. You can do that by turning the valve on the supply line that leads to each spigot.
What if a pipe bursts?
Immediately turn off the water, using the shutoff valve for the individual pipe or the house's main shutoff valve. It's found where the water supply enters the house, usually near the water meter.
The meter is usually along the basement wall nearest the street.
If you don't have a basement, the shutoff is probably near the water heater but might also be under a sink.
If you're lucky enough to discover a frozen pipe before the pipe breaks, shut off the water first, just in case the pipe has already split and you don't know it. Then try thawing the frozen section by directing warm air from a hair dryer parallel to the area you suspect is frozen, or by pointing an infrared heat lamp or space heater at the section.
As a last resort, wrap rags around the pipe and pour on boiling water, but be prepared for a mess and slow results.