Dough rises because gas bubbles from the leavening agent are trapped by gluten in the flour, creating little pockets in the dough. I’ll discuss gluten and leavening agents separately.
Gluten is a protein in wheat flour that becomes elastic when the flour is mixed with water and kneaded. Generally, the more you knead dough, the more elasticity you add to it. That is why, incidentally, that some recipes like biscuits instruct you to “quickly mix wet and dry ingredients”: in these recipes, you want the biscuits to turn out flaky, not bread-like, so you try to minimize the gluten’s elasticity by not overly mixing the dough.
Leavening dough can be accomplished by fermentation (with yeast or starter), chemical agents (baking soda or baking powder), or by a process (whipping egg whites). Of the ways to leaven baked goods, however, fermentation is by far the most interesting.
Yeast breads, prior to cooking, are really living colonies of tiny organisms that eat carbohydrates (flour and sugar) and produce carbon dioxide and alcohol as waste products. This process is called fermentation, and the results should be familiar to any beer drinker. In fact, bread is a lot like beer, except that with bread, you are more interested in the carbon dioxide gas resulting from the fermentation than you are with the alcohol. Consequently, I consider bread and beer cousins, if not brothers – certainly part of the same beloved family, anyway.
Yeast can be purchased either in packets or in a jar. If you can, buy the jar. It’s a better deal, has less packaging, and is more likely to be in your refrigerator when you need it than those pesky packets. (Yeast, at least jars of yeast, should be refrigerated after opening.) Also, yeast as purchased always has an expiration date on the label – check this before you buy it. I never remember to do this, and probably 3 times out of 4 I come home with expired yeast. Apparently the yeast cops are out having doughnuts, instead of diligently checking grocery store shelves like they should be. It would serve them right if they got flat doughnuts. You can still use expired yeast, though, it just sometimes takes more pampering to get the colony organized and flourishing.
Thinking of the dough as a living creature is a useful paradigm: the yeast colony needs some care to survive and prosper. Yeast likes warmth; it grows more quickly at room temperature than in the refrigerator, as you might expect. A little warmer than room temperature is usually ideal. Do keep the little guys and girls out of drafts. It is annoying to listen to the dough sneeze and hack because it caught a cold due to your leaving the bowl next to the window in January. Don’t let it get too warm, though, or you’ll kill them. Yeast genocide is not something you want on your conscience, at least until you bake the loaf. At that point you can claim you were only following orders. Seriously, though, don’t raise dough in the oven with the oven on at any temperature. If you are in hurry, you can turn the oven on to its lowest setting for a couple minutes, then turn it off and put the dough in the oven to rise. If the rack is too hot to touch, it’s probably too hot for the dough.
As with any other pet, you need to get rid of your dough’s waste products. Luckily, with dough this task is much more pleasant than cleaning your cat’s litter box. The yeast needs you to knead it (and wants you to want it, and…). Besides working the gluten, kneading the dough pops the bubbles of carbon dioxide in the dough and allows the gas to escape, thus allowing the yeast colony to live long and prosper. The alcohol that the yeast produces just gets mixed back into the dough, and you can’t really get rid of it. Who would want to, anyway? It’s alcohol. Punching the dough down with your fist while the dough is rising in a bowl accomplishes the same thing, by the way. The “punching down” step isn’t included in recipes just to allow you to take out your frustrations on critters smaller than you. We bake them for that.