First, heat a pot with a few inches of water in it, I used a 3.5 quart saucepan. Add vinegar to the water. This helps tighten up the egg.
You don’t want boiling water. You don’t want simmering water. You want very hot water at the point right before it simmers. Bubbles, not boiling.
Break an egg into a small dish. It is easier to slide the egg in from a dish and you can focus one hand on the next step and not worry about using both hands to crack your egg. Unless you’re awesome at cracking an egg one handed (when I try to crack eggs with one hand I end up with shells in my eggs).
Make a whirlpool with your spoon. Slide the egg into the middle of the whirlpool with your other hand.
This is my favorite part from a set of instructions I found on Smitten Kitchen:
Don’t freak out. (I almost did.)