I do it like this
Two-Minute Mayonnaise | Serious Eats : Recipes
I always add salt and pepper and some sugar or maple syrup with the egg yolk, water etc. And I like to use high oleic sunflower seed oil (much lower in omega 6) rather than EVOO (which becomes very bitter).
Anchovies added at the start are excellent too, as is a crushed clove of garlic.
Water is what will cause your mayo to emulsify and become thick.
Sometimes folks get frustrated making mayo because it is not properly emulsifying and thickening up, and understandingly think that if they were to add more water, it would just be even thinner.
It is counter-intuitive. The extra TB or so of water (whether in the form of vinegar, lemon juice, mustard, or just water) is what will make it become a thick, stable emulsion.
If you are having trouble, try adding an extra TB of water to whatever mixture you were trying with before.
I have this awesome mini food processor from kitchenaid, cost around $35 and I use it all the time. Awesome for mayo, in fact can get too thick. I pour the olive oil through the small hole in the top, and I plug the larger opening or else you will be wearing mayo. Also great for blender hollandaise (and chopping eggs, onions, celery, etc.). Easy clean up as well.
This recipe has always worked for me. Take her advice both on letting the egg and lemon juice sit for at least an hour in the food processor, and take your time when you drizzle in the oil (takes me anywhere from 3 - 5 minutes). Makes fabulous mayo!