Clean the entire surface of the furniture. Open the windows in and turn on fans for ventilation in the area you're working in.
Dip an extra-fine steel wool pad in vegetable oil. Buff the area and go with the grain.
Dampen a clean cloth with water. Dust the area lightly with flour. Blot the oil and flour to remove the excess. Flour helps absorb the oil.
Buff and polish the surface with a polishing compound.
Scrape out the char with a curved knife or sandpaper, avoiding the surrounding areas of the table. Work slowly to avoid mistakes. Brush away the char as you work with a clean cloth dampened with water.
Remove the last layers of char from the table, using sandpaper. Once you see unaffected wood in the dent, remove the last bit of char and clean the area with a lightly dampened cloth. Allow the area to dry.
Fill the dent in the wood with a wood filler, using a putty knife. Use light to medium pressure and work with the putty knife at an angle. Allow the filler to set.
Sand down the area with an extra-fine steel-wool pad. Brush away dust with a damp cloth. Buff and polish the area.
Stain the area to match the rest of the table, using a clean, soft brush. Use a feathering motion in the direction of the grain. Allow to dry.