Soap and Water
Use a gentle cleanser, such as dish or hand soap, and a bottle brush. Fill the bottle with warm water and scrub. Don't use hot or cold water, as sudden temperature changes could crack the glass. For stubborn dirt, you may want to let the bottle soak overnight before scrubbing. Also try adding a gentle abrasive to the water, such as rice, sand or coarse salt. Cover the opening of the bottle with a cork or your thumb and shake vigorously. Rinse to remove all traces of the abrasive materials and detergents.
Stronger Cleaning Solutions
If your antique bottle needs more cleaning, you may need to use stronger products. Use a solution of equal parts vinegar and water, or a dark carbonated cola, in place of strong acids which may damage your bottle. Scrub with a bottle brush and follow with a detergent to remove any traces of the cleaning products. Let dry upside down so that moisture isn't trapped inside the bottle.
Polishing and Professional Options
If cleaning products don't have the desired effect, you may want to try more drastic cleaning methods. If your bottle is valuable, you should have it cleaned by a professional, who will "tumble" the bottle in a special machine, which cleans and polishes the glass. At home, try purchasing a rock polishing compound at a craft supply store. Apply a thin solution of the compound to your bottle and gently polish with a cloth until the stain is minimized or removed. Rinse with room-temperature water.