Fill the teapot halfway with cold water. Finish filling the teapot the remainder of the way with white vinegar.
Set the teapot atop the stove, and bring the water and vinegar solution to a boil.
Remove the teapot from the burner and allow the solution inside to remain for 24 hours.
Empty the pot after 24 hours, and scrub the interior with an old toothbrush. Be sure to work the brush in and out of the spout as well.
Fill the teapot to the top with cold water. Place the teapot once again atop the stove, and bring the water to a boil.
Empty the teapot, then rinse it thoroughly with fresh water.