Hello Kbarber. I'm Cindy. Make a solution of equal parts of water and vinegar. Soak a cloth in this solution and wrap it around the faucet. Hold it in place with Saran wrap. Leave it overnight. In the morning just remove the wrappings and rinse with clean water. You can do the same thing with your shower head.
Do not use vinegar if your counter is granite or marble. Vinegar will etch it.
Here's a good video tutorial: https://www.youtube.com/watch?v=gdcbF3bqdh0