I have been making homemade mayo for about a year. I started mostly because it is so cheap and i hate getting caught without. I have found that a palm mixer works the best and if you use a countain the same diameter as the base of the mixer you will also get a better result.
break an egg into the container and add
1 tablespoon dry mustard
2 tablespoon vinegar
1 teaspoon of salt
and white pepper if you have it (i never do so i use black)
lastly add one cup of canolla oil
put the mixer into the contain and start it as the you see the clouds of mayo form go up until your at the top. Seal container and store in fridge like you would store bought.
It is to the point that my kid prefer the homemade and even their friend have made comments on how they prefer it.