If a faucet and sprayer were both previously working properly, and now water only flows from the sprayer and not from the faucet, the problem is internal. This problem can happen with older faucets whose inner mechanisms have become worn, and it can happen with newly-installed faucets. The repair can be simple, taking just a few minutes of time, or it can involve you disassembling the faucet body.
An aerator that is clogged with sediment and debris may prevent a faucet from working properly. The aerator is the small, removable end of the faucet spout, and it is the easiest part to repair. Simply unscrew the aerator with your hand and rinse its screen and other parts clean with water. You can also scrub the parts with an old toothbrush. The aerator itself is small, and so are the other parts inside it, so be careful not to drop any pieces down the sink while handling it. Place a rag over the sink drain before removing the aerator to prevent losing anything in the drain.
Stuck Diverter Valve
The job of the diverter is to switch the flow of water from the faucet spout to the sprayer. A stuck diverter valve prevents the water from switching back to the faucet from the sprayer. Turn the shut-off valves underneath the faucet all the way to the right, shutting off the water, before working on the faucet. Follow your particular faucet's owner's manual to properly disassemble the faucet, then locate and replace the diverter valve -- its exact location varies from model to model. If debris is blocking the diverter valve, clean the debris away, reassemble the faucet and test to see if it now works.
If a washer within the faucet is out of position, it can completely or partially block the flow of water through the faucet. To find out if a washer is the problem, you will once again need to shut off the water to the faucet first. Familiarize yourself with your faucet's anatomy, using the owner's manual, and use the manufacturer's instructions to locate the washer. If the washer is damaged or brittle, take it to a home improvement store to make sure you obtain the right replacement washer.
Prevent the buildup of debris in the faucet body or aerator that may lead to water not flowing through the faucet as it should. When you initially install the faucet and connect the water lines underneath it, remove the aerator and fully open the faucet's hot and cold water valves. Often, the water that flows out of the faucet will be discolored with debris and sediment that has settled in the line. Once the water coming out of the faucet clears up, turn off the faucet and screw the aerator back on.