Turn the faucet handles counterclockwise to the open position. Turn the handles as far as they will go to fully open the valves and to allow any ice dams to flow through. Keep them open for the time it takes until full water pressure is pouring from the faucet.
Once the water valves are open, you can simply wait for the water in the pipes to thaw if the temperatures around the pipe rise above freezing. This will take the longest time and you will need to stay close by to turn off the valves once the ice melts.
Blowing warm air from a hair dryer over the surface of the frozen pipes will melt the ice blocking the water rapidly. You can also use an electric space heater or a heating pad wrapped around the pipes. Be very cautious of overheating the flammable materials under a sink. At first, the water will just trickle from the faucet; but as the ice blockage shrinks, the water pressure will increase until the flow washes the leftover ice from the pipe.
Cover the pipes with insulating wrap if they are near exterior walls or in noninsulated basements. For old houses with poor insulation, a temporary fix is to turn on the faucet to a slow drip when you know the temperatures are dropping below freezing. The flow of water keeps pressure from building when ice forms, and it causes ice to form more slowly to boot. Another remedy, for instances when you need to travel for several days and you fear sub-freezing weather will occur while you are away, is to drain the water pipes before you leave.