In a small bowl, whisk egg yolks with 1/2 the vinegar or lemon juice and the mustard, until thick. Add a little salt to taste.
Whisking constantly, add the oil drop by drop. After you've added about 2 tablespoons, pour in the rest of the oil in a thin stream while whisking. Add the rest of the vinegar or lemon juice and keep whisking until thickened.