There are a few different ways to repair a faucet that is leaking at the base. One simple way involves replacing the O-ring. This can be done easily while the faucet is disassembled. It is also a relatively inexpensive fix and shouldn't drain your emergency home fund. 

Check the valve

 If you are dealing with a continuous leak, it's likely that you need to replace the valve or the check valve. The exact parts will depend on the faucet model number, so consult your manufacturer's parts catalog or Customer Service for help identifying your model number. If you can't find the part number, try a plumber's grease or plumber's lubricant. If the leak has spread to the base spout, you may need to replace several parts, including the handle.  

Remove the spout

 First, you need to remove the spout. This can be done by lifting the spout. Then, use a channel-lock pliers to loosen the connecting ring. Be sure to protect the finish of the fixture with adhesive tape. 

Repair kits contain this grease

 You can then reassemble the faucet and replace the o-ring. Remember to take photographs or note all parts you remove, and make sure that the new parts match the original ones. You may need a flashlight or a hex (allen) wrench to help you. Before you start removing the o-ring, use some plumber's grease on it. Most repair kits contain this grease, but it's important to use it properly to avoid damaging the finish.  The most common cause of a brushed steel pull out kitchen tap leaking at the base is a faulty O-ring. Often, the O-rings are worn out or have mineral deposits, which prevent them from being able to create a tight seal. A faulty O-ring means water leaks out of the cartridge, which means it's no longer watertight. 

Replace the valve/spacer

 Sometimes, the cause of a faucet leaking at the base is more obscure. A continuous leak after a faucet has been turned off is the result of dirt or debris collecting in the valve/cartridge. In other cases, the leak is caused by a worn-out check valve/spacer. Replacing the valve/spacer can solve the issue for a short period. You can also replace the seals, which vary depending on the model of the faucet. If the leak is caused by a damaged ceramic disc cartridge or a cracked cartridge, you can repair the problem by cleaning the components and re-inserting them. Then, you can replace the cartridge or the O-rings if necessary. You may need a plumber's grease to replace the disc cartridge. Another common cause of a faucet leaking at the base is worn-out washers or loose O rings. These components wear out when the faucet is overtightened. If you can find the leak, then it may be a simple matter of tightening the fittings to stop the water from leaking. You may also need to replace the shut-off valve.