I didn't have any mayonnaise for my kids' sandwiches, so I just made some for the first time ever. Oil is fairly cheap in bulk, and we have a supply of fresh eggs from our hens.
It took a couple tries. Here is a quick tip: if you have a food processor, it probably has a tamper, and the tamper probably has a tiny hole at the bottom of it.
The purpose for that hole is to drip oil sloooooowly into the emulsion as it is being beaten, to prevent the emulsion from breaking. The food processor--a gift from our wedding--seems to work the best.
A wire whisk did not work at all. It never got thick. I think that is where the problem started...it was never completely emulsified. But with the food processor, it got quite stiff like store-bought, only a different color due to different ingredients.
The ingredients are 1 egg yolk, 1/2 tsp dry mustard, 1 cup of oil (I used half canola, half rice-bran oil), 1 TBSP lemon juice or white vinegar, and salt and pepper or paprika to taste.