Bathroom vanity and kitchen sink faucets have three basic causes for low flow.
Faucet Supply Valves
The supply valve, located under the sink, may not be fully open.
The typical faucet supply or “stop valve” has a handle on it that opens the valve when turned to the left (counter-clockwise), and closes the valve when turned to the right (clockwise). Make sure the stop valve is fully open by turning it to the left until it stops turning. Do not force these valves, as they become easy to break as they age.
While looking under the sink, inspect the tubing or pipe leading from the stop valve to the faucet. If the tubing is flexible plastic, ensure it does not have a kink in it, or has been crushed during assembly. If it is kinked or crushed, it should be replaced. Close the stop valve by turning it to the right (clockwise) until it stops, then remove the tubing and take it to the plumbing department to ensure you get the correct replacement.
Most faucets have an aerator, or filter screen, that may be clogged.
This aerator is most often threaded onto the end of the faucet. When removing the aerator, use a cloth around the aerator to protect it from tool marks. While looking down at the top of the faucet, you will thread the aerator to the right (clockwise) to remove it. Inspect the debris found on the inside of the aerator screen. Most often, you will find sand, hard mineral buildup or, more rarely, plastic chips. If the material rinses off easily, set the aerator aside and run the cold and hot water for two minutes each, with the aerator off. This will flush the remaining material out of the faucet. Mineral deposits may be hard to remove. You can use a commercial de-scaling product such as CLR or Lime-Away, or soak the aerator in a 50/50 solution of white vinegar and water for two to three hours.
If you have two or more faucets with low flow, and the aerators are clean in both of them, it is unlikely that you would have two failed faucets. While it does happen, it is far more common for debris or scale to affect several fixtures.
If the flow is not restored, the problem could be a clogged or defective faucet itself. Many faucets can be cleaned, but the process varies by brand and model of faucet. The basic steps are to turn off both hot and cold water supplies to the faucet. Remove the handle and then access the valve cartridge, if equipped. If there is a valve cartridge, it will be within the body of the valve, and removing the handle will reveal screws, a nut or a clip that is removed to thread or pull the faucet cartridge out of the faucet. Once it is removed, inspect it for sand, mineral buildup or other debris. If the o-rings or gaskets look worn, take the entire cartridge to the plumbing department to ensure you get the correct repair parts. Some cartridges are available as a complete replacement unit.
The article on Low Water Pressure for the whole house will have more information on looking for blockages in the main water supply lines. Usually, this results in low water pressure at every fixture.