Mistakes happen all the time with painting. Drips, splashes and spills can end up anywhere, including in your granite sink. Left unnoticed (as often happens during busy home improvement work) paint spills dry and are more difficult to get up. You have several products to choose from that will make the clean-up a lot easier. These products soften the paint, loosening it from the hard surface and making paint spills much easier to scrape up and wipe away.
Carefully scrape away as much of the paint as you can, using a plastic scraper or a razor blade knife. Dried latex paint may come up easily this way. Be careful not to scratch the granite.
Put on rubber or nitrile gloves to protect your hands from solvents. Open a window in the room for ventilation.
Saturate a cotton ball or a swab (for small spots of paint) with white spirit, or spray your spray lubricant directly on the paint. You can (alternatively) use commercial paint removers if you choose, but spray lubricant and regular white spirit are usually good enough for small paint spills.
Scrape the area again with the scraper or knife. Wipe the area with damp paper towels to remove more of the paint. If it is not all coming off, reapply spray lubricant or white spirit and wipe it again.
Rinse the sink with cool water to remove traces of paint, spray lubricant or white spirit.
Latex paint will wipe right off a granite counter if the paint is still wet--just use warm water and dish detergent on a clean sponge. Oil-based paints will also wipe up easier when still wet, but you may still need to use white spirit.
Fumes from most paint removers, including products like water-displacement spray lubricant and white spirit, are very flammable. Be very careful using these--keep windows open and do not use these around candles, lit cigarettes, pilot lights or other flame sources.