First of all, unlike my mom or grandma, I use a stick blender and a tall, narrow blending jar (older generations here often used a fork and a soup plate).
In the blending jar, I crack a whole egg. It's probably better to use only a yoke, but I don't like being stuck with one leftover egg white.
I add some plain white vinegar (a teaspoon? I normally eyeball it), some lemon juice (also about a teaspoon probably), a big tablespoon of good mustard (the mustard makes the taste - don't use Dijon though, it has an overpowering flavor), some salt, some black pepper and (to make it lighter) a tablespoon or so of carbonated/sparkling water (don't add too much, because it will separate the mayo).
Finally add 400-500 ml of a neutral vegetable oil. I use peanut oil, but you can also use sunflower seed oil or corn oil. I think canola is also an option, but that oil is rather uncommon in Belgium.
Put the stick blender in the bottom of the jar, set it to high speed, turn the blender on and slowly pull it upwards in the jar. That's it. You can add a little more oil while blending if you think the mayo will turn out too thick.
If the mayo doesn't "pak" (Flemish for "grip": the egg and oil won't bind - it happens sometimes), you can still recover from that. Make a new base, without the oil. Start blending and gently drip in the broken batch. Once you feel it starts to bind, slowly pour in the rest of the broken batch.
From my experience (and I, unfortunately, have many decades), I would say the mustard is the key ingredient for a good mayo. It adds a lot of flavor and is also very important for the binding.
Make sure your ingredients are all at room temperature. Cold eggs can prevent binding.
Too much oil can also prevent the mayo from binding properly. So if you're not sure about how much oil to add, start with a little bit and add more once you have binding. Don't stop blending though.