If at all possible, it's best to start with organic eggplant seeds, to ensure that you are receiving untreated seeds from plants grown without the use of synthetic pesticides and fertilizers. Here are some of my favorite sources for organic eggplant seeds.
Sow eggplant seeds in cell packs or small pots, 1/4 inch deep. Water them well, cover loosely with a plastic bag or a plastic seedling flat cover to retain moisture, and place them in a warm spot―on top of the refrigerator or on seedling heat mats would be perfect. Keep the soil moist. You should see condensation on the inside of your plastic bag or dome. If you don't, then it's time to water with a gentle mist to avoid dislodging the seeds. The seeds will germinate without additional heat, but it will take longer.
Generally, eggplant seeds germinate in 7 to 14 days. Once they've germinated, remove the plastic cover and place your pot or flat under lights or in a bright window.