You can clean granite with soap and water. Avoid anything acidic - it can etch the stone.
All stone should be sealed to protect it from acids. If you laid a piece of lemon on the stone within minutes it would take the shine away. This is the beginning of etching the stone. A good sealer will also stainproof the stone.
I recommend Hydrex from Tenax. It dries invisible and protects your investment. Think Scotchgard for stone. Here is the link to it:
http://www.defusco.com/tenax-impregnator-and-sealer-liter-p-2095.htmlWhen sealing stone tiles, seal them after they are laid but before you grout. The sealer will act as a grout release so the grout doesn't stick to the stone. Another advantage of a mineral based sealer such as Hydrex.
Glad to be of service,
Mark