Mayo is easy. If you have a stick/immersion blender here ya go. You can thank me later.
One caveat: if you are making mayo with extra virgin olive oil, the blender methods cause bitterness. I didn’t believe it at first, but I tried it side by side, and the blender mayo was noticeably more bitter than the hand whisked one. Apparently, it has to do with polyphenols. According to Cook’s Illustrated, regular olive oil doesn’t suffer the same problem.
Personally, when I make olive oil, I tend to like the pure EVOO kind, which many people find a bit too olive oil-y for their tastes. For me, mayo is just a way to get the flavor of olive oil and a bit of lemon into my sandwich without making a giant mess. But experiment with different recipes. Add lots of garlic to it, and you basically have aioli. Try chopping in different herbs. Play around with your acids (lime mayo is popular in the Hispanic community, for instance.)
The blender methods are foolproof, with my one warning about EVOO. The hand whisking method isn’t difficult, but it does take patience and a little bit of practice to know what you’re looking for. Generally, the rule is one egg yolk to a cup of oil. You start by beating your egg yolk until it turns lemon yellow. Then you add your oil slowly, a few drops to a teaspoon at a time, and beat it until it’s incorporated into the yolk. When your mixture looks homogenous and not a glop of oil on top of an egg yolk mass, you add a little more oil. Continue in this manner until you’re about halfway through with the oil. At this point you can drizzle it in more liberally. Drizzle a bunch of oil in while whisking vigorously. Stop. Incorporate all the oil into the yolk until it’s homogenous, repeat.
When you first start out, take your time and be sure all the oil is incorporated into the yolk before adding more oil. As you get better, you’ll be able to “read” the emulsion and add much more quickly. If the emulsion breaks (turns into oil and yolk) and can’t be re-emulsified by hand, all is not lost. You can try emulsifying it with a blender (defeating the point of doing it by hand), or you can start with another egg yolk, and drizzle the broken emulsion into it slowly, and whisk, just like in the other steps of the mayo process, except instead of drizzling in oil, you’re drizzling in the broken emulsion.
Oh, and start with room temperature eggs.
Mustard, oil, vinegar, lemon juice, salt, pepper, etc., can be added at stages during this process. I usually beat in a little mustard with the yolk in the beginning, along with about a teaspoon of lemon juice. I add more lemon juice at the end. Some people do it all in the beginning. Some add as they go along. It all seems to work.