Dissolve the yeast in the 3/4 cup warm water. Add the 3 cups warm water; stir in flour and sugar. Beat with an electric mixer on medium speed until smooth.
Cover with 100-percent-cotton cheesecloth. Let stand at room temperature (70 degrees F to 80 degrees F) for 5 to 10 days or until the mixture has a sour, fermented aroma, stirring 2 or 3 times every day. (The fermentation time will depend upon the room temperature. A warmer room speeds the fermentation process.) When the mixture has fermented, transfer to a 2-quart or larger plastic container with a tight-fitting lid. Refrigerate the starter until needed.
To use the starter:
Remove starter from the refrigerator and stir thoroughly. Measure the amount needed and bring it to room temperature before using. (The cold starter should be the consistency of buttermilk or thin pancake batter. If necessary, add water to thin the starter after it is stirred and before it is measured.)
For each cup of starter used, replenish the remaining starter by stirring in 3/4 cup all-purpose flour, 3/4 cup water, and 1 teaspoon granulated or brown sugar. Cover and let mixture stand at room temperature for at least 1 day or until bubbly. Refrigerate starter for later use.
If you have not used the starter within 10 days, stir in 1 teaspoon granulated or brown sugar. Repeat every 10 days unless starter is replenished.