Bring a small pan to a boil. The water level should be high enough to fully cover the eggs once in.
Take the eggs out of the fridge and using a large spoon, gently place them in the boiling water. Avoid any shock that could break them open.
Let them cook on medium heat for 4 minutes. Consult recipe story and notes for variables that can change the target cooking time.
Using the same large spoon, take the eggs out of the pan and place them in the egg cups.
Break the top part of the shell with a knife, hitting around the shell in circle, then poke through the egg and remove the shell cap.
Add hot sauce, or salt and/or pepper, and eat immediately.
Notes
Some people like the white to be fully cooked absolutely no runny white at all. If that is the case, I recommend a cooking time of 4 mins to 4 mins and 30 seconds. You may have a slightly cooked yolk as a result. Cooking is a continuum. There is no border between white and yolk, so within 10 seconds, the line between the two can be crossed. I prefer my eggs to have a more liquid yolk at the expense of having a few areas of runny egg white left. This is the 3 mins 45 seconds to 4-minute mark. These times are assuming:
you are using large or very large eggs
the eggs come into the boiling pan at fridge temperature
you don't live in very high altitude (2000+ meters, 5000+ feet)
Changes from these assumptions will impact how fast your eggs cook. Smaller eggs cook faster, and so do those coming in at room temperature. High altitude makes water boil at a lower temperature, requiring longer cook times.