There could be many reasons why water won’t come out of a faucet, the first thing you should check is if there is water available at other fixture to determine if it is just the one faucet or, the problem exists else where in the home. Fixtures at a lower level may seem to flow at a reduced pressure then stop this would just be water draining out of the higher pipes. For simplification purposes this article will focus on a single faucet not having water come out.
If the problem exists only at one faucet and neither hot nor cold water comes out you should check the aerator on the end of the faucet to see if it is blocked by debris. Unscrew the aerator and remove it from the end of the faucet then turn on the faucet to see if water comes out. If water comes out the aerator is clogged with debris and needs to be cleaned or, replaced.
On kitchen sink faucets with side sprayers you should also check to see if water comes out of the side sprayer only but not the spout with the aerator removed. If water comes out of the side sprayer but not the spout a sticking diverter valve would be the culprit. The location of the diverter valve varies with different makes and models of faucets with it being located under the spout, under a screw on cap that holds the spout on, and under the faucet just to name a few possibilities. You can often look up your faucet on-line at the manufacturer’s website to see where it is located. Often the diverter can be removed allowing a quick temporary fix but it will allow water to come out of both the spout and the side sprayer when the side sprayer is used.
On pull out style kitchen sink faucets the hose can be unscrewed from the head and you can see if water will come out of the hose. If water comes out from the hose look for a clogged screen where the hose connects to the head. In some cases the head may need replacing.
After checking out the faucet you can shut off the angle stops under the sink then disconnect the lines feeding the faucet. With a bucket in place to catch the water turn on the water to see if any is coming out to supply the faucet. It would be a good idea to find where the main shut off is located before doing this because angle stop valves are notorious for being cheaply constructed and sometimes not shutting off properly. If the valve does not shut off and you cannot reconnect the supply you will need to shut off the main valve. This is also where you would start if only hot or, only cold water comes out.
Once you have gotten past the faucet and supplies you are basically tracing pipes back to a point where other fixtures are connected and not affected. Problems could be any number of things ranging from valves shut off, old galvanized pipes clogged with rust, and in colder climates in winter you may have frozen pipes supplying the one affected faucet. You can find information on thawing frozen pipes on 411 Plumb. You may need a plumber to help you figure out what is going on with your water supply to the faucet.