The heat has failed and it is freezing.

Deal with the pipes before you deal with the temperature. Open the cabinet doors under every sink on an exterior wall, let the faucet furthest from the main drip steadily, and close the doors to rooms nobody is using. Then work through the simple checks on the heating before you call anyone.

People can put layers on. A burst pipe turns a cold night into a flood.

First: the pipes

The pipes at risk are the ones in unheated space and against outside walls: under sinks on exterior walls, in crawl spaces, garages, attics, and any run in a wall that faces the weather.

Open the cabinet doors under those sinks so house heat reaches the pipes.
Let a faucet drip, ideally the one furthest from where the supply enters. Moving water is much harder to freeze, and an open faucet relieves the pressure that actually splits pipes.
Do not close off rooms containing plumbing. Closing doors saves heat, but not in a room with pipes in the wall.
If it is going to be a long outage, consider shutting the water off at the main and draining the system. That is the definitive answer and it is what an empty house should have done anyway.

What to do if one has already frozen, and what to do if it has already split.

Then: the checks worth doing yourself

Ten minutes, before paying for a service call.

The thermostat. Batteries, set to heat, set above the room temperature. A dead thermostat battery is a genuinely common cause of no heat.
The breaker. Even a gas furnace needs electricity for its controls and its blower. Check the breaker and any switch on or near the unit, which often looks like an ordinary light switch and gets turned off by accident.
The filter. A blocked filter is the single most common cause of a system shutting down on a safety limit. If it is gray and matted, replace it and try again.
The gas supply, if other gas appliances also have nothing. If the stovetop does not light either, the problem is upstream of the furnace.
The condensate line, on a high efficiency furnace. They produce water, and a blocked or frozen condensate line trips a safety switch and stops the unit. A frozen external condensate pipe is a very common cold snap failure and thawing it with warm cloths sometimes fixes it entirely.
The vents and returns. Blocked returns and closed vents in too many rooms make a system trip.
The outdoor unit, on a heat pump. If it is buried in snow or encased in ice, clear around it gently.
The pilot or ignition, on an older system. Follow the instructions on the unit itself, and only if they are printed there. More detail on the sequence.

If any of that produces heat, you have saved a service call. If it does not, you can tell the technician what you have already ruled out, which shortens their visit.

Then: keeping people safe

Layers, hats, and blankets rather than one big heat source.
One room heated and used, with the door closed, if the whole house cannot be warmed. Not a room with vulnerable plumbing in the walls.
Electric heaters only, and one per circuit, plugged into a wall outlet rather than an extension cord. How to run one without starting a fire.
Eat and drink warm things. It matters more than people expect.
Check on anyone vulnerable, in the house and next door. Cold is most dangerous to the very young, the very old, and anyone with a chronic condition.
Leave, if it is not safe. A house that cannot be kept above freezing with an infant or an elderly person in it is a reason to go somewhere else, and it may be a reason your policy pays for it. What additional living expenses covers.

The fuller list for getting through it.

Getting someone out

In a cold snap every heating technician is busy, so:

Call early, not at nine at night.
Say if there are vulnerable occupants, which moves you up most priority lists, and say if the house is at risk of freezing.
Have the make and model of the unit and any error code on the display.
Ask about the service call fee and whether it is credited against work.
If you rent, call the landlord or agent as well, in writing. No heating in a freeze is an emergency repair obligation nearly everywhere.

The short version

Pipes first: cabinet doors open, a faucet dripping, and no closed doors on rooms with plumbing in the walls. Then check the thermostat batteries, the breaker, the filter, and the condensate line before calling. Layers and one warm room for people. Never a stove or an unvented heater, ever.