The hardest part is the prep of the eggplant. Traditionally, the eggplant is roasted over a wood fire until it is baked through and the skin has charred. After it cools, the soft insides are scraped out and it is mashed with the other ingredients using a ghanuj, or pestle. Baba in Arabic means father and Baba Ghanoush is just "father of pestle." See Wiki for more historic details.
Anyway, we live in an age where a kitchen has modern conveniences and we tend to be in a hurry. So, I use a gas stove, microwave and food processor to produce a Baba that any Caliph would smack his lips over--in a fraction of the time!
Step 1: Roast and Cook the Eggplant
Get a good char on the skin, but don't worry about cooking the eggplant through.
After you get a good char, put the eggplant in the microwave and cook it for 1-2 minutes. You will know it is done when it collapses (see photo).