I use a hand blender with a whisk attachment. It was useless until I discovered the right container for the job - a metal flask kind of like these:
http://www.amazon.com/Stainless-Ste...6699721&sr=8-13

If you're not familiar with mayonnaise making, this is what you do:

Put the egg yolks in the container, and add some of the salt, spices and acid. I use salt, lemon juice and sauerkraut juice.

Start whisking. Add fat drop by drop, and then in a thin stream, always slow enough that it doesn't build up without becoming emulsified.

That's about it, except that you can adjust the acids and flavors at the end.

There's one more thing I do, though: I usually add more egg yolks along with more salt and lemon juice. I pour the mayonnaise out, start with a new yolk, and then add the mayonnaise just as I added the fat. This is also how you fix mayonnaise that's "broken." I find that doing it in a couple of cycles makes it smoother, which is somewhat of an issue because chicken fat can get grainy.