If a faucet leaks, usually the simple replacement of a rubber washer can fix the problem. Changing a fixture is not difficult if you take these steps.
Measure the size of your fixture from the center of the holes made in your sink. A common example would be a two handled faucet with center nozzle where the faucet holes are four inches apart. Choose a replacement based on size, functionality and look.

Turn off the water below the sink. Turn on the faucet to drain any existing water. Undo the supply lines from the existing faucet from below with a wrench. Remove the supply lines, either braided stainless steel or copper, then undo the faucet from the sink itself. If space below your sink is tight you might need a tool called a basin wrench that is more maneuverable. Lift off the fixture. Clean out the crud, scrubbing hard for a tight fit.