EGG - THE COOKING BASICS
A common mistake when cooking eggs is overcooking. When the egg gets overcooked, it gets rubbery, that is, it loses its natural softness. Prolonged cooking should be therefore avoided, so the egg proteins don't "overdenature" and disperse the water that is bound in a network all around them. Eggs cooked in their shells should be timed perfectly. One good way to avoid overcooking is by heating up the water with the egg to boil, then removing it from heat, and put a lid on the pot. Soft cooked eggs of medium size require then 4 minutes of cooking, and the hard cooked eggs - about 12-14 minutes. After the time has passed, pour out the hot water and replace with the cold water (if you want to cool the egg).
When it comes to eggs that are cracked open, there are several tricks to take advantage of.
Poached eggs should be cooked in a hot but not boiling water to avoid the highest temperature shocks, especially for the most sensitive egg proteins, which could separate the yolk from the egg white. Also, addition of vinegar (5% of total volume) will help coagulate the egg proteins quicker (due to acidity) so they will not have to withstand the heat for too long time.
Custards are even more sensitive to heat, in a way. Often, people get scrambled eggs instead of a fine liquid custard and that's simply because they have overheated the egg proteins. Around 80 C/175 F is the limit for the proper coagulation of the egg proteins, and at this temperature it is not injudicious to strain the custard into a cold clean bowl. Simply removing the pot from the heat at 80 C/175 F may not be good enough since the proteins will continue to cook in the residual heat.