Mayo is an emulsion of oil which is tiny oil droplets suspended in some other kind of liquid, usually an acidic one like lemon juice or vinegar. Lecithin found in egg yolks and mustard help to chemically stabilize the emulsion. Air incorporated into the mix makes it light and creamy.
CAUTION: Use of kitchen appliances with blades that spin in excess of 2 billion rpms is dangerous. Know what you are doing in the kitchen and clean up the mess afterwards.
Step 1: A few things from the pantry...
Juice of half a lemon
A squirt of mustard
An egg yolk, use the egg white in another recipe
Oil, the usual bland vegetable oil
Salt and pepper
And for the added zip, you can add:
minced clove of garlic
minced leafy herbs like parsley, choose a good herb to pair with the food the mayo will be used on
Note that I don't usually measure anything when I cook. Get a feel for what works.