Really good mayo is easy to make. This recipe is an adaptation of a recipe by Alton Brown on the Food Network. I modified the recipe for my tastes but the basic recipe is from Mr. Brown.
Let the eggs come up to room temperature to ensure a good emulsion.
Place the oil in a squeeze bottle with a narrow tip.
In a glass bowl, whisk together the egg yolks and dry ingredients.
In a separate bowl, combine the lemon juice and vinegar. Then whisk half of the lemon juice and vinegar mixture into the egg yolk mixture. Begin whisking the mixture briskly, then begin adding the oil a drop or two at a time until the liquid begins to thicken. That is the emulsion that you are looking for. Now, increase the flow of the oil to a very thin but constant stream until half of the oil is added.
Add the remaining lemon juice and vinegar mixture to the emulsion and whisk to incorporate.
Continue whisking while adding the remaining oil in a thin but constant stream.
Notes
Safflower oil is my prefered oil for making mayonnaise. It is neutral tasting and relatively inexpensive. Corn oil is also often used.