First you have to properly beat or whisk all the ingredients except for
the oil. Then, most importantly, the oil has to be added literally drop
by drop for the first 3 tablespoons at least. This is what gives
the mayonnaise the thick consistency. If you add too much oil at
once, or just mix all the ingredients at once, the sauce "splits" as we
call it in cooking school, what happens is that the oil separates form
the rest of the ingredients and you can beat or whisk that mixture for
hours, it will never develop the thick consistency of mayonnaise, the
only way to fix a broken sauce is to put a tablespoon of water into a
separate bowl and pretend that the water is the new egg, salt and
vinegar mixture, and that the split sauce is the oil. Drop by drop add
the split sauce to the water and you'll get your mayonaise back.