Yeast, although it may not look like it, is actually a living organism–a type of fungus that consumes sugars in food and gives off gases in exchange. These gases are what make foods containing yeast, like breads and other baked goods, rise correctly. Because yeast thrives on sugar, typically recipes that use yeast call for at least a small amount of sugar to get the yeast started. However, most recipes with yeast can also be made with sugar substitutes without any loss of quality.
Consider your recipe. Yeast does require some sugar to work, but sugars are found in many different types of foods, including fruit, flours and cornstarch. Yeast can use the sugars in these foods in place of regular table sugar. Unless the recipe you are trying to make contains nothing with natural sugars in it, you can safely replace the sugar with a non-sugar substitute. Alternatively, you can use a sugar substitute like honey or molasses, which behaves in much the same way as sugar.
In many recipes, you are directed to add a small amount of sugar to warm water before adding the yeast and allowing it to come to life (or "bloom"). If you are using a caloric sugar substitute like honey, simply add it at the same point as you would sugar. Keep in mind that honey and molasses are not quite as sweet as sugar, so you may need to add a slightly larger amount to achieve the same effect. However, these sweeteners also add a very distinct flavor of their own, so be sure to take that into account.
If you prefer to use a non-caloric sugar substitute, you can skip step two entirely. While sugar does help yeast bloom faster, it is really not necessary. Just add the yeast to warm water and allow it to sit for a few minutes, then add to your recipe. If you are concerned that your yeast may not be active and need to see them foam to be certain, add a small amount of flour to the water. The sugars in the flour will give the yeast something to feed on.
Proceed with your recipe, but if you used a non-caloric sweetener, pay close attention to rising times. The more sugar in your recipe, the happier your yeast will be and the more gas it will produce, creating a faster and higher rise. However, your baked goods will still rise without sugar–it may just take a little longer. Allow yourself 1 1/2 times the recommended rising time, and keep an eye on the rising action. If your dough fails to rise, you may have had old yeast. Try again with fresh yeast. If you are still having rising issues, add extra yeast to the recipe to make up for the lack of sugar.