I do!
My number one tip is to always have your ingredients at room temperature. If they are too cold it can be a disaster!
Next, choose your oil - sunflower is the most neutral tasting. If you want to use olive oil, make sure it is the mild and light one - never extra virgin, it tastes vile as mayo! Cold pressed rapeseed oil is good but is very expensive and not everyones taste. If this is your first attempt I would start with sunflower.
I think a handheld electric whisk is important too. Doesn't need a fast setting.
I make my mayo thus....
Whisk together one egg yolk, a capful of cider vinegar, a teaspoon of dijon mustard and salt and pepper to taste.
The you simply whisk whilst drizzling the oil in. A little at a time is the key and keep adding oil until you get your desired consistency.
Once it is made you can stir in any other flavouring you fancy. I have tried lemon juice, garlic, harrisa, smoked chilli paste and curry powder so far and they are all lovely!
Good luck!