My son gets very nervous when he has to separate eggs. I was taught to use the two halves of the shell method. The link shows you what is, without a doubt, the simplest, most tidy way I have ever seen to separate an egg. I recommend that you just open a fresh bottle of water and empty it out before you try to do this. I'm not sure I'd trust how clean the bottle would be after drinking from it, no matter how hard you scrub. Using a plastic bottle to separate an egg.
I'm almost tempted to bake an angel food cake, just to give it try. There is little as much fun as applying science to your baking (creating a vacuum is what sucks in the yolk, if you weren't aware.)