Fill the carafe half full or more with warm water. Add one teaspoon of dish detergent and stir the solution with a bottle brush or a sponge on a handle.
Scrub the insides of the carafe with the brush or handled sponge. Then pour out the sudsy water.
Fill the carafe two-thirds full with warm water. Add white vinegar until the carafe is nearly full. Keep this mixture inside the carafe through the next step.
Clean the outside of the carafe with a warm sudsy sponge. Rinse the sponge and pour a few tablespoons of white vinegar on it. Rub this over the outside of the carafe.
Dry the outside of the carafe with a soft cloth. Clean and dry the lid in the same manner. After 15 minutes to half an hour, dump out the vinegar and water solution. Keep the carafe open to dry. If the carafe has a large enough mouth, you may hand dry it with a towel.