How do you clean soot stains from a stone fireplace surround?

Is there a certain cleanser or some home made concoction?

try one of those mr clean scrubby pad things or even a little bit of bleach and water and some good ole elbow grease
Elbow grease and any of the following chemicals alone, do not mix...... Bleach, Simple Green, Oxy Clean Use rubber gloves, put down plastic to protect the area, and use a soft bristle brush. If you have allergies or are asmatic, where a mask.
they have a cleanser called boric acid it works they sell at home depot :)
I was watching a show on TLC and they used a big red rubber eraser. I tried it on our brick and it worked OK. It's slow going and it can be tiring on the arms.
Use a solution of 9 parts water and 1 part muratic acid or swimming pool acid, make sure you wearing rubber gloves and are in well ventilated area. put up a fan to blow fresh air where you are working, the fumes are nasty. use a plastic brush, cover things in surrounding area to protect from splash. rinse with water when clean. This is a harsh solution so be very careful. It does work very well.