Check the faucet and surrounds for dripping or pooling water. This helps find the leak.
The handle leak may be caused by a worn-out O-ring or cartridge. Try tightening the handle to stop the leak.
Spout leaks may be caused by a worn washer. Replacing the washer often fixes the problem.
A leak from the connections underneath can cause water stains around the faucet base. Check supply lines and connections for dampness.
Clogged or loose aerators can cause leaks. Check the aerator for debris and damage.
Pressurized water can leak. Measure and adjust pressure with a pressure gauge.
The cartridge may be the problem with a single-handle faucet. Check multi-handle faucet valve seats and washers for damage.
If you can not find the leak, turn off the faucet's water supply, disassemble it, and examine for internal concerns.
If the leak persists after the aforementioned measures, call a plumber. They can diagnose and fix difficult issues.