Liquid spills can penetrate the surface of the countertop so try to clean these spills up immediately to prevent staining.
Clean the surface with a neutral cleaner, stone soap, or mild dishwashing liquid and warm water. Rinse well and be sure to use a soft, clean cloth at every step.
Generally you can remove stains with a paste mixture consisting of flour, dishwashing liquid, and water (for grease stains use hydrogen peroxide instead of dishwashing liquid). You should apply the paste to the stain, cover with plastic wrap, and let sit overnight. Scrape the paste away with a wooden utensil and rinse well.
Finally, you should seal your granite countertop every couple of years to help maintain that like-new surface and shine you love. Be sure to ask your installer for recommendations on sealing and general maintenance for your specific type of granite. Enjoy!