I second the recipes from katylester and wasatusay.
I am a cooking and food fanatic, have several good friends and family members in the industry, and my mom is the best cook I know. I learned to do this from my mom.
beating fast enough to get the emulsion going is the key. Otherwise you will be sad wiht a broken sauce. I love to do everything by hand but getting mayo started by beating by hand with a whisk is something that's always evaded me.
mayo (may be scaled proportionately:
one fresh egg yolk
juice from 1/2 lemon, approximately (lemons vary a lot... start with less juice and then add more to your liking)
pinch of salt
freshly ground pepper
a pinch of dry mustard (optional)
oil (vegetable, olive, etc, if you use melted butter instead, then it would be called hollandaise rather than mayonaise... with olive oil and garlic, it becomes aioli)
in a food processor or blender or mixer with whisk attachment, put everything but the oil. blend at high speed until very blended. Then, add the oil SLOWLY, like drop by drop at first, while the machine is running until it starts to come together (smooth and creamy, not broken and lumpy). Once it's started to emulsify, it's much more stable. You can add the oil faster now until it reaches your desired consistency. All amounts are approximate, and once it comes together, you can adjust the seasonings... more salt, pepper, lemon, etc. adding fresh herbs can be nice too.