Put sugar and water on burner over medium heat, stirring constantly until it begins to boil.
Take out the spoon, and with a brush dipped in cold water, wash down sides to keep sugar crystals from forming.
Cover and boil the mixture for 5 minutes.
Add cream of tartar and cook until mixture reaches soft ball stage, which is 238 degrees on a candy thermometer. If you don't have a candy thermometer, you can test the stage by dropping a small amount of the mixture in cold water. If it forms a soft ball, it is ready.
Turn the mixture out onto a marble slab dampened with water.
Let it stand until you can make a dent on the surface with the handle of a wooden spoon.
Work the candy back and forth with wooden spatula until it becomes a white, smooth, creamy paste.
Knead mixture with your hands and place in a medium sized bowl.
Cover closely with damp cloth and put in a cool place for 24 hours.
If you'd like to add color or flavor to the fondant, dot it with food coloring/flavoring after the 24 hour period and knead fondant until color is evenly distributed.
Roll on a cool, non-stick surface, and use to decorate your baked goods.