I used to make it by hand, but never again, this recipe is excellent. It's from Julia Child's The Way to Cook.
Machine-made Mayonnaise
For 2 to 2 1/4 c.
1 "large" egg
2 egg yolks
1 tsp. dijon-type prepared mustard
1/2 tsp. salt
2 tsp. freshly squeezed lemon juice and/or wine vinegar (I like cider vinegar)
1 1/2 - 2 c. best quality oil- peanut, olive, or other oil- all one or a mix
(I use canola)
Freshly ground white pepper
More mustard, salt, lemon juice and/or vinegar, as neede
Droplets of sour cream, sweet cream, or water- to lighten the finished sauce if it's too stiff
Place whole egg, the yolks, and the teaspoon of mustard in the container of a food processor; process 30 seconds with a plastic blade, 15 with a steel blade. Add the salt and lemon juice/vinegar and process 15 seconds with a plastic blade; 7-8 with the steel blade.
Witht he machine running, start adding the oil, pouring it in a thin stream of droplets-keep your eye on the stream to be sure it is going very slowly. Keep the machine always running, and when you see that the sauce has thickened, you may add the oil a little faster. Stop the machine after 1 1/2 c. or so of oil, and check on the sauce: if it seems very thick, add droplets of lemon juice or vinegar, and taste for seasoning. (You do not need to use all the oil; if you like a yellower sauce, for instance, 1 1/2 c. may be sufficient.) Continue with the oil, if you plan to use all of it. Season as needed.
I like my mayo very yellow, so I don't use much oil. You'll see and hear when it becomes an emulsion. You won't want to buy premade mayo again.