In a mixing bowl or the cup for your immersion blender (I recommend the immersion blender unless you need an upper body workout)
Mix 1 egg yolk with:
1/2 tsp of salt (fine like popcorn salt)
1/2 tsp dry mustard
2 pinches of sugar
In a separate bowl combine
2 tsp lemon juice
1 tblsp white wine vinegar
Add half the lemon juice mixture to the yolk mixture and beat the eHell out of it with a whisk (or use the immersion blender). Add:
1 cup oil (safflower is what I use, corn is good, but olive oil gives a nice taste too) a teensy bit at a time.
The mixture will lighten and thicken (form an emulsion) and you can step back the whisking a bit. Then you can add the oil as a steady drizzle.
Add the rest of the juice/vinegar once you've added half the oil.
Once all the oil is added then cover and let sit for an hour or two at room temperature to set up. Will keep for a week in the fridge.
* * *
You can dress the recipe up by adding other spices and flavors (celery seed, rosemary, chipolte peppers, red pepper, increase the sugar)
Or using different oils (substitute a tablespoon or two of safflower oil for chile oil)
Or different acids (lime juice, basalmic vinegar)
As long as you have the egg, the oil, some acid, and a few dry ingredients (to hold it together) the recipe is infinitely changeable.