The easiest method is always to watch someone else do it. If you have been gifted with the task then no matter how sophisticated or expensive the products you use the techniques are all very similar. Dish soap is still the best, yes, the same stuff you use everyday for the dishes you eat from. Streak-free dish detergent is economical and plentiful, simple and safe to use, and will get the results you seek.
A dish-rag soaked in hot sudsy water should be used to saturate the granite surface. Allow a few minutes for the hot soapy water to work its magic. Scrub with same soapy rag shortly thereafter to remove any build-up or stubborn grime followed with a rinse or two of hot water from a soap-free rag.
For Heavy Cleaning:
Further agitate the soaking-wet surface with a coarse cloth or mildly abrasive ScotchBrite style pad, (white, red, and blue pads only) rinse as usual. Stains can be removed by cutting open a granular automatic dishwasher capsule and gently rubbing a small amount at a time into the stain and repeating until successful.
After any cleaning regiment and after your stone has dried some streaking may still remain. Streak-free dish soaps seem to minimize this. Use a clean cotton rag, microfiber cloth, or white color ScotchBrite pad to buff away cleaning product residue that remains.
Periodic buffing when surface is dry with extra-fine(000) steel wool followed with a slightly damp clean cloth to pick up steel wool particles left behind. A spray and shine liquid wax like "Zep" buffed with a clean cloth will add some glossy brilliance.
Read more about sealing and preserving your natural stone in my blog titled "Granite Myths and Truths" Enjoy your natural granite stone! firstname.lastname@example.org