How do you separate an egg - is that your question? Because you can actually buy egg whites in the grocery store. They are sold in cartons as an egg "substitute." Some of these substitutes are 98% or 99% egg white with added nutrients, salts, flavorings, etc. But some (All Whites is one brand) are nothing but egg white.
But, if you're willing to roll up your sleeves and get to work, and are asking about the nuts and bolts of separating eggs, we're here to provide tactical support.
old-fashioned way to separate an egg is to give it a sharp crack on the edge of a bowl. Holding the egg upright over the bowl, pry off the top half of the shell. Some of the egg white spills over into the bowl, but some of the white and all of the yolk stay in the bottom half of the shell. Then carefully pour the yolk into the empty half of the shell, and much of the rest of the white falls into the bowl. Repeat the process of pouring the yolk from one half of the shell to the other and you very quickly have a clean yolk in one half and all of the white in the bowl. This method has fallen into disfavor because of concern that the shell may be infected with harmful bacteria and letting the egg white slop all over the shell on its way to the bowl is an unsafe practice.
Another method - and the one we prefer - is to crack the egg into a bowl, reach in with your scrupulously clean fingers and lift out the yolk. You may have to transfer the yolk from one hand to the other a couple of times, as well, to get all the white off. But you get a very clean yolk with this method. We are secure enough in our egg cracking that we will crack all the necessary eggs into one bowl first, before reaching in to remove all the yolks (and only having to wash our hands twice). But if you are concerned that you may break a yolk, you can certainly crack and separate the eggs one at a time, putting the yolks in one bowl, the clean whites in another, and using a third for the actual separating.
Some people find fishing around for egg yolks with their fingers a little icky. For them there are hosts of egg separators on the market, ranging from less than $1 to more than $10. (We assume the expensive ones work ten times as well or ten times as quickly.)