I use one egg yolk, a splash of lemon juice or vinegar, a wee bit of salt and pepper, and half a cup of oil. Use extra-virgin olive oil if you want to die of the pleasure, and money is no object. For merely fabulous mayo, blend olive oil with canola oil.
Whisk everything but the oil together. Then start to add the oil drop by drop, whisking until it’s gone in between each drop. When things start to thicken up a bit, you can start pouring it in a very thin stream, still whisking madly. It should thicken up nicely and become paler. (If you use all olive oil, it won’t get as light as store-bought.) It takes longer to explain than to do–just be sure to whisk like your life depended on it, and you’ll be fine.
This doesn’t last very long, so I make in small quantities. But, truly, it is an entirely different entity from Hellmans. You’ll never go back.