Leavening gives baked goods lift. (The word leaven means “lighten.”) And all leaveners work the same way: by producing carbon dioxide bubbles that are trapped by the dough’s structure, and in turn, make the dough rise.
Yeast is available in three forms: fresh yeast, active dry yeast, and instant yeast. Fresh yeast is usually sold in foil-wrapped cakes, and is the trickiest to use; it must be proofed — made active in liquid — before using. Active dry yeast is fresh yeast that has been pressed and dried. It is sold foil packets; you don’t need to refrigerate it, because the packets are sealed for a shelf life of up to two years (check the expiration date before using, though). Instant yeast, also called fast-acting, fast-rising, rapid-rise, and bread machine yeast, is the yeast almost everyone uses now (it’s what I use in all of my recipes calling for yeast). It can be added directly to the dough at almost any point. Neither active dry or instant yeast requires proofing to do their job, but you can proof them if you like to make sure they are still vital.
To proof any kind of yeast, mix it with a small amount of warm (not hot) water; if you like, add a pinch or so of sugar. If the mixture doesn’t begin to foam or bubble up within 5 to 10 minutes, the yeast is dead and you need to try again with new yeast.
Baking soda (sodium bicarbonate) produces bubbles of carbon dioxide in the presence of moisture and acid, usually an acidic liquid like buttermilk, yogurt, or vinegar. This reaction occurs on contact, so once baking soda is added, whatever it is you are baking needs to get into the oven as soon as possible. You want those bubbles formed in the oven, not on the counter, so add it in last, mixed into the flour to ensure even distribution through the dough or batter. If you are tinkering with a recipe, be careful not to add too much baking soda, because it’s quite salty. Plus, whenever you add more baking soda you must add more acid; too much of either or both, and the whole thing could become unpleasantly acidic.
Baking powder is baking soda with a dry acid added to it, along with some starch that keeps the baking powder dry and inert until it’s activated. Single-acting baking powder generally contains cream of tartar as the acid and is activated by moisture, so the batter or dough should be baked as soon as possible after being mixed. Double-acting baking powder also contains slower-acting sodium aluminum sulfate, which releases the majority of its carbon dioxide when exposed to heat in the oven, for a second leavening. So batters using double-acting baking powder can sit at room temperature for a few minutes before being baked — but just a few. Too much baking powder can give baked goods a bitter taste and — if the air bubbles grow too big and break — cause them to collapse.