1. If you will be separating more than one egg, you will need three bowls. The good news is that one of these will be the bowl you will be beating the egg whites in. The other bowls can be quite small.
2. Crack the egg, holding it over one of the smaller bowls. Then, shifting the yolk from one side of the shell to the other, let the egg white flow into the bowl.
3. When as much of the white is removed from the shell as possible, put the yolk into one of the other dishes and pour the saved egg white into the mixing bowl.
Here is the reason for the three bowls: When you are separating the eggs, it is possible that the yolk may break and some of the yolk will fall into the egg white in the bowl. However, even the tiniest bit of egg yolk will keep the whites from forming the foamy texture you want when beating them. By putting each egg white into another bowl as you separate the eggs, you avoid having all the egg whites spoiled should a bit of yolk get in them.If you want to see some videos with a couple of other methods—including using your hand instead of the shell to do the separating, go to http://www.wikihow.com/Separate-an-Egg
One more thing: if you do get egg yolk into one of the egg whites, DON'T throw it out! If you have no other baking to do right away, an egg out of the shell like this can be tightly covered and refrigerated for a day or two or used for an impromptu scrambled egg supper.