When poaching eggs, the most important thing to remember is that stealth is of the essence. Because birds are herd animals, if they become distressed, they will quickly alert other members of the flock, thereby causing complete cacophony and crushing the plans of all but the boldest of poachers. Soft-soled shoes are highly recommended, as are sturdy garments which will withstand climbing and a variety of weather conditions, depending on the species of bird involved.
But seriously. Assuming one is referring to how to prepare the dish known as poached eggs, rather than how to steal eggs by dead of night, there are two ways to poach eggs. One can use an egg poacher, a special type of cooking pan which has been specifically designed for this purpose, or one can poach eggs in a pan of simmering water. The end result, in both cases, is an egg with a thoroughly cooked white and a slightly runny inside which can be eaten plain, on toast, or over an assortment of dishes ranging from rice to steamed greens.
An egg poaching pan has two parts: the pan itself, and an insert with roughly egg-shaped depressions. To poach eggs in such a pan, the pan is filled with water, and the insert is placed on top. When the water starts to boil, eggs can be gently cracked into the divots in the pan to poach. The moist heat of the boiling water from below will cook the eggs to the desired consistency, while the divots will ensure that the eggs cook neatly, rather than splaying as they tend to do in simmering water. It is a good idea to butter or oil the divots before cooking, so that the poached eggs will neatly slide out when they are finished.
To poach eggs in a pan of simmering water, a basic frying pan should be used, filled with a few fingers-widths of water; heavy frying pans such as those made from cast iron tend to produce better results. As the water starts to boil, a splash of plain white vinegar should be added, and the water should be turned down so that it barely simmers before eggs are gently cracked into it. Some cooks prefer to crack their eggs onto spoons or into small bowls, so that they can slide the eggs into the water; the goal is to jostle the eggs as little as possible, so that they poach neatly. After the whites of the eggs have solidified, they can be ladled out of the water and served.
Poaching eggs using the second technique can require some trial and error, as it takes time to perfect this poaching method. Adding vinegar to the water helps the whites stay together, and lightly simmering rather than actively boiling the water also encourages the eggs to hold their shapes. The advantage to the second technique is that any liquid can be used, for adventurous cooks who want to poach eggs in wine or stock for specific dishes.