There are several ways to leaven bread, you can use yeast from both commercial and wild sources as well as several other methods such as shown in the following links Soda Bread with Vinegar, Salt Rising Bread, and Old Ways to Leaven Bread.
Baking powder if stored in a cool area has a long shelf life. BYU has tested baking powder that is over 20 years old and found it to still be effective. However regardless of the shelf life it is still possible to run out of any product. So what do you do if you run out of baking powder?
If you have both baking soda and cream of tartar on hand, you can make you own homemade baking powder. Both of these items are available in grocery stores or in bulk on the internet. When stored separately they have an indefinite shelf life.
To make the equivalent of 1 teaspoon of double acting baking powder, mix 1/2 teaspoon of cream of tartar with 1/4 teaspoon baking soda (two parts of cream of tartar to one of baking soda). This homemade baking powder will work very successfully but you must remember that when you use it, get whatever you’re baking into the oven right away.
To store homemade baking powder: Add a teaspoon of cornstarch or arrowroot to the mixture, and stir. This will absorb any moisture from the air, and prevent the baking powder from reacting before you need it. Store the baking powder in an airtight container.
If you only have baking soda, there are other products you can substitute for cream of tartar to make homemade baking powder.
Other acidic ingredients such as lemon juice and vinegar will work as substitutes for cream of tartar. For every ½ tsp of cream of tartar called for in the recipe, substitute it with 1½ tsp of lemon juice or vinegar. Some people, feel that when lemon juice or vinegar is used in this manner, it can change the flavor and texture of the end product.
Sour milk, buttermilk or yogurt when mixed with baking soda will work. Mix ½ cup of whichever dairy product you choose with a 1/2 teaspoon of baking soda.
If you use the last suggestions, remember to take into consideration the extra liquid and the fact it may cause changes in taste and texture.