Cut the ends off of the garlic, peel it, and either chop it or put it through a garlic press. Put the garlic in a mortar and pestle with the salt and grind it into a paste.
In a heavy mixing bowl, whisk (you can use an electric whisk) the egg yolks, lemon juice, and garlic mixture together until well combined, about one minute.
Start adding the olive oil, drop by drop, whisking all the while. You can add it a bit faster as you go along, but as with mayonnaise, the key to success is going very slowly at the start. When you are done adding the oil you can adjust the seasoning as suits your taste.