You need a saucepan, a hob, a slotted spoon and a slightly old egg. Fresh eggs don't poach well as the white will disintegrate.
Put the saucepan on the hob. Fill with water. Bring this water to a rolling boil (really bubbly). Don't bother adding vinegar or salt. Put the whole egg in, shell and all, and leave for about 15 seconds. Take it back out (with the slotted spoon). Now crack the egg into the water. Boiling it before means you are less likely to damage the yolk!
I really hate slimy whites so I usually leave the egg in there for about a minute and a half. If the water is spurting about everywhere, turn it down slightly so you don't rip the egg apart, but the bubbling will help to stop the egg sticking to the bottom of the pan. Don't poke the egg or try to mix it or anything until it ought to be ready. Then, very gently pick it up with the slotted spoon, allowing as much water as possible to drain away.
Eat with buttered toast, rostis, fried leftovers or my personal favourite, mashed potato and bagged salad mixed together and fried. Mmm, fried salad.