Summarize:

Use 1 egg yolk for every 1 cup (240 mL) of liquid you need to thicken. Whisk the yolks until they are loosened. If you are using a whole egg, separate the whites from the yolk before whisking. This will temper the eggs and increase their temperature. The hot water will heat the eggs without making them too hot and causing them to cook. Your sauce should be hot when you add in the eggs. Whisk the sauce continuously while it simmers. Make sure to scrape the sides and bottom of the pan as you stir. This will ensure that the sauce doesn’t stick to the pan or burn. Do not let the sauce boil for too long. Once it reaches its boiling point, 1 minute will be plenty of time for the sauce to thicken.  Since you are using raw eggs, you much check the temperature of your sauce to eliminate the possibility of bacteria. The sauce must be at least 160 °F (71 °C) before it is safe to serve.
Whisk the egg yolks in a pan over low heat. Add 2 US tbsp (30 mL) of hot water to the egg yolks. Whisk the eggs into your sauce and simmer over medium heat. Allow the sauce to boil for 1 minute.