You can put eggs either in cold or boiling water. If the eggs are taken directly from the fridge, it is best to put them in cold water. Otherwise, they might crack.
Cooking times, counting from when the water starts to boil lightly:
In cold water
Soft/runny eggs 1 – 2 minutes
Medium cooked eggs 4 – 5 minutes
Hard boiled eggs 7 – 8 minutes
In boiling water
Soft/runny eggs 3 – 5 minutes
Medium cooked eggs 6 – 7 minutes
Hard boiled eggs 9 – 10 minutes
Soft/runny eggs should not be rinsed in cold water. Instead, leave them for a couple of minutes after you take them out of the water. This way, their inner temperature continues to rise, and the consistency gets to be lagom: the yolk is soft and loose, and the white just starts to set.
Medium and hard boiled eggs should be rinsed quickly in cold water, if they are to be eaten warm. If you are going to peel them, it is best to put them in cold water until they are cold.