A variety of ways to cook eggs

Whether fried, boiled, poached, baked or steamed, eggs that are cooked whole, without stirring or beating, shares a need for gentle heat to keep whites tender and yolks moist. 
Aside from this constraint, the methods have little in common; each makes different demands on the cook. 

When eggs are fried in a shallow layer of butter or oil, for example, the temperature must be set low to prevent the undersides from burning while the tops cook. For eggs that are to be served sunny-side up, the tops can be firmed quickly by covering the pan with a lid that will reflect heat downward. Alternatively, the eggs can be turned, either with a spatula or by tossing them. A variation of shallow frying is to shirr eggs by setting the undersides in melted butter on the stove top, and finishing the eggs in the oven.

Deep frying an egg helps to solve the problem of uneven cooking by applying all-around heat. However, to preserve the egg's tenderness, the temperature of the oil or fat must be markedly lower than is the case when deep frying most foods and the white must be neatly and quickly folded around the yolk to protect it from overcooking. Shells protect eggs cooked intact in water, a process called boiling, although, in fact, the water must be at a simmer to avoid toughening the whites. Because the cooking is concealed, accurate timing is essential: It may vary from three minutes for an egg to be eaten from the shell to 10 minutes for an egg that is to be peeled.

For poaching immersing eggs in hot liquid without the protection of their shells the temperature should be below a simmer: Bubbling liquid would break up the whites. The best way to control the temperature is to bring the liquid to a boil, then turn off the heat before adding the eggs. Covered with a lid, the pan and its contents stay warm enough to cook the eggs in a few minutes. Only the freshest eggs should be poached; their firm whites will cling to well-centered yolks. Shaping is no problem when eggs are cooked in containers by baking or steaming. The use of containers also makes it possible for other ingredients, such as vegetable purees, to be cooked along with the eggs. Baking is most commonly done in an oven preheated to about 350-F. Steaming is done in a covered water bath, placed either in the oven or on the stove top.

Frying: Fast Cooking in Shallow Fat
When eggs are cooked in a thin layer of fat, heat is directed at them only from below, If the eggs are served sunny-side up, the cook's task is to ensure that the tops of the eggs cook at the same time the bottoms do, so that the thick rings of white surrounding the yolks set before the undersides burn. Basting the eggs by spooning fat over them will help cook the tops. In addition, you can cover the skillet with a lid to reflect heat downward.
Alternatively, you can turn eggs over midway through frying, so that both the tops and the bottoms are brought into contact with the heated surface of the pan (right, bottom). You will find it easiest to reverse eggs with the aid of a spatula, but some virtuosos prefer to flip eggs by tossing them, in the pan. Because of the difficulty of flipping eggs simultaneously, or of turning several in one pan, both of these techniques work best with one or at most two eggs. 
Whichever frying method you choose, you should add the eggs to the skillet as soon as the fat is hot to prevent it from burning and spoiling the taste of the finished dish. The fresh flavor of melted butter marries well with eggs; so does the fruity tang of olive oil. Most cooks break the eggs directly into the fat, but some prefer to crack eggs onto a plate and then slide them into the pan so that if a shell accidentally crumbles, the fragments can be easily removed. After cooking the eggs, you can mix a little vinegar or lemon juice with additional melted butter in the pan to make a simple sauce. 

Shirring eggs is an extension of the pan-frying technique: The eggs start to cook on top of the stove, and are then placed in an oven or under a broiler to set the white. Gratin dishes just large enough for one or two eggs are traditionally used for this method. For the second stage of cooking, cream may be added to the eggs to enrich their flavor and give them a melting smoothness.