Soot is slightly oily and clings to most surfaces it lands on. Removing soot requires using a product that can loosen it and break it down. Vinegar is such a product and is safe for most surfaces.
Fill a clean plastic or glass spray bottle half full of white vinegar. Fill the rest of the bottle with water.
Spray this mixture on the sooty surface such as a glass fireplace door or walls. Wipe it clean with a damp sponge or damp paper towels. If this mixture does not seem to affect the soot, use the vinegar full-strength instead of diluted with water. Use a scrub brush on harder materials such as bricks.
Rinse the area with a damp sponge or damp cloths. Dry the surface with clean, dry cloths. If you notice any darkening of the cloths, indicating the presence of soot, go through the whole cleaning procedure again. Soot may be trapped in porous surfaces and it may take several attempts to fully remove it.