How to fix kitchen sink faucet?
Remove it from the bench and soak it in lime remover (white vinegar, dilute muriatic acid, etc)
Disassemble it, and clean the parts.
lubricate it with Vaseline (or other petroleum jelly)
Replace any worn seal found, reinstall it
There should probably be some sort of circular gasket or o-ring between the base and the benchtop.