This is a true emulsion sauce.
1. Separate an egg yolk into a bowl and add 1 tsp of lemon juice (or white wine vinegar) and salt and pepper.
2. Whisk the egg yolk until it thickens and aerates.
3. Now, very gradually, take one cup of olive oil, add about 1 tsp of oil and whisk together. Keep adding a little more each time until the mayonnaise starts to thicken, or emulsify.
4. Once you have achieved this, add the oil in bigger amounts making sure it is completely incorporated before adding further.
5. If it gets too thick, add a few drops of lemon juice or hot water to "cut in back", then continue to add the oil.
Practice makes perfect so give it a try.