Fill a small sauce pan with water and place on stove on medium heat until there are bubbles forming but it is not boiling. Lower heat but make sure water stays hot.
If you have access to a strainer, place a small strainer over and empty bowl. Crack your eggs into the strainer and let the loose whites fall through. This should happen naturally, you won't need to agitate the strainer.
Place this strained egg into another small bowl and set aside. The strained egg should still have a significant amount of egg white around the yolk. Repeat with another egg and place in a small bowl.
In your small sauce pan with hot water, add a tablespoon of vinegar. Carefully pour your strained egg into the hot water with bubbles (but not boiling or even simmering). I typically try and poached 2 eggs at a time so carefully place you second strained egg in the same sauce pan.
Cook for about 2-3 minutes until eggs are cooked to your liking. White cooked with a runny yolk. Use a slotted spoon to remove the eggs from water and place on a paper towel lined plate.
I typically empty the water in the small sauce pan and reheat a new batch or water with an additional tablespoon of vinegar for the next two eggs.