To boil eggs:
Hard-boiled: Cover eggs in a saucepan with cool water and bring to the boil, then remove from the heat (or, if you are using an induction hob, simply turn it off). Let stand covered for 9-10 minutes (less if you're not using them right away, as they'll continue to cook in their shells).
Soft-boiled: Reduce cooking time to 8 minutes.
I like simple methods that bring out the best flavour and texture, so these are my preferred methods of boiling and poaching eggs.
To POACH eggs --
Traditional method, free-floating:
Nearly fill a small saucepan with water and bring to the boil. Meanwhile, crack the egg or eggs into a shallow dish. Stir the water with a wooden spoon or spatula to get a kind of whirlpool motion going. Lower the dish to the surface of the water and slip the eggs in as quickly as you can. This will cool the water: bring it back to a rapid boil. Lower the heat slightly to a less ferocious boil and cook for a few minutes more, until the egg white has turned into a shaggy white ball. Remove with a slotted spoon. Note: many people like to add vinegar to the water as they say that it helps the egg white to cohere rather than be dispersed through the water. I find the benefit negligible or unnoticeable, and I don't like the vinegar flavour, so I don't bother.
Contemporary method, in a silicone cup:
Fill a pot with about 1 inch of water (roughly 3 centimeters), and bring to the boil. Meanwhile, crack the egg into the cup (slicking it with oil for perfect release is optional and not really needed). Place the cup in the water, cover the pot, and reduce the temperature to a moderate boil. On an induction hob, I find that setting the timer for seven minutes at 6 on the dial gives me a perfect egg -- soft-centered and slightly oozing yolk and tender, well-cooked albumen (induction hobs allow you to be really precise.) One benefit of this method, apart from the neat form of the egg and the fact that you don't lose any to the water, is that it's easy to judge whether the egg is done to your liking or not. If it's underdone, just stick the cup back in the water for a bit more cooking.