For novices, baking can often be a frustrating exercise. Far too often you follow a recipe precisely, only to have the resulting cake prove to be a resounding dud. There are many reasons for cakes not to rise, and with time and practice you'll learn most of them. In practice, they boil down to a few basic mistakes.
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Trusting the Recipe
The most fundamental mistake made by most novices, and some bakers who should know better, is trusting the recipe. All too often recipes are written or transcribed under deadline pressure, and consequently errors find their way into print. Internet recipes are especially trouble-prone. Before baking a recipe for the first time, it's helpful to compare it with others of the same type. If the ratios of eggs to fat, sugar to flour or liquids to flour are consistent in three recipes but significantly different in a fourth, the fourth is probably in error.
Even when the recipe lists all the ingredients in their correct proportions, it's easy to make mistakes while measuring. Professionals usually measure and set out all their ingredients before starting to minimize the risk of errors. Measure carefully in good-quality measuring cups and spoons, following the recipe's guidance if it gives you specific instructions. Your grandmother may have just estimated ingredient quantities by eye, but you probably don't have her experience. A large number of cake failures are due to poor measuring. This is why professional recipes are generally measured in weight, which allows for better accuracy.
Not creaming your butter and sugar long enough can make your cake dense, by not incorporating enough air into the butter. Too little liquid in the batter makes it dense and heavy, as does too much flour. If your baking powder is old, or if you don't use enough, there may not be enough leavening to rise the cake. If you're making a sponge cake, even a small amount of oil or yolk in the whites keeps them from foaming as they should. You also need to fold the whites gently into the batter to avoid losing the air.
Problems in Baking
If your cake fails to rise adequately and sets with a crater in the middle, your oven may not have been hot enough. Check it periodically with an oven thermometer to be sure it's accurate. A sudden vibration can make your cake fall if it has risen but not yet become firm. If you're baking a sponge cake or angel food cake, it'si mportant not to grease the sides of the pan. Your cake needs to cling to the sides. Otherwise it won't be able to support its own weight until the baking is finished.