Thick deposits of soot and grime can be scraped directly off the glass using a single-edged razor blade or box cutter. Make certain the glass is completely clean before trying this method. If possible remove the glass or the door from the fireplace itself, then scrape the glass gently over a drop cloth or newspapers. Most thick deposits will come off easily.
Vinegar works well to remove soot stains from fireplace glass. HGTV suggests combining 1 cup of vinegar in 1 gallon of warm water, and sponging or spraying it directly onto the glass surface. Wipe the glass clean with a lint free cloth or old newspaper, to avoid streaking, clouding and bits of fabric or sponge stuck to the glass. Vinegar Tips suggests removing fireplace grime with undiluted distilled vinegar. Scrub trouble areas using a brush, and blot up the dirty vinegar with a lint-free towel.
Detergent solutions also work to remove soot from fireplace glass. Combine about a tsp. of liquid dish detergent with a gallon of warm water, and sponge or spray onto the glass. Remove the liquid and the soot with a lint-free cloth or newspaper.
While ordinary glass cleaners struggle to remove soot, commercial cleaners designed for use on glass are better at getting rid of carbon. According to HGTV, these can be purchased in specialty fireplace supply stores. Commercial glass cleaners often come in paste form. According to Hearth.com, they should be rubbed onto the glass using an elliptical motion. Get the paste into the corners and along the edges of the glass. Allow this cleaner to dry for a few seconds, then use a soft cloth to rub the paste and carbon off of the glass.