Empty the contents of the decanter. Rinse it out well with warm water.
Fill the decanter with white vinegar. If the decanter is stainless steel, use equal parts white vinegar and water.
Let the vinegar sit in the decanter overnight for glass pots, or 20 minutes for stainless steel pots. Dump out the vinegar mixture from the decanter.
Fill the kitchen sink with hot, soapy water. Scrub the inside of the decanter with a soft cloth and the hot, soapy water.
Sprinkle some baking soda onto a sponge if the burn spots remain. Scrub your glass or stainless steel decanter gently with the sponge and baking soda until the burnt coffee is gone. Wash the decanter again in hot, soapy water.