I was struck pretty much dumb the first time I tried it. It's so easy! So fast! You just put the ingredients in a jar, shove the stick blender down in, and pretty much before you can say "mayonnaise," it's done!
So that's how I make mayo now; it has never failed me in quality or speediness. It's magical to watch it form in the jar!
Measure into a wide-mouth pint jar (I use the line on the jar):
1 cup neutral veg oil
1 Tbsp. lemon juice
1 Tbsp. white wine vinegar
1 tsp. prepared mustard (dijon is called for, but I just use my homemade)
1/2 tsp. salt
Put immersion blender in jar, firmly on bottom. Hold blender to bottom of jar while blending until you see creamy mayo rising up to 2/3 of the way. Pull the blender up through the mixture to get the top layer of oil emulsified. Give a few more blasts on the blender through the whole jar, but do not overbeat. Done! Put the lid on and store in the fridge.