Take your wood table outside if possible so that you have maximum airflow while you work. If you must keep the table inside, open nearby windows and doors.
Remove some of the soot on the surface of the wood with the floor attachment of your vacuum. Just hover over the surface; don't actually place the floor attachment on the wood.
Create your own cleaning solution by mixing 1/2 cup of ammonia with 1/2 cup of warm water. Dip a white cloth in the cleaning solution and use it to wipe down your wood. Always wring the cloth out so that the wood does not become soaked, which leads to warping.
Dry the wood immediately after cleaning. Use a lint-free towel. Examine the wood to see if there are any traces of soot.
Wipe the wood table down with a chemical sponge if you noticed any lingering soot. Chemical sponges are sometimes called dry cleaning sponges. They are sold in cleaning supply stores and are capable of removing soot and soot odors.