How do you get essential oils to emulsify in water and alcohol?

Dissolve it in alcohol (preferably 96%) and then slowly mix some water in as long (and as much) as needed to get a 'misty' kind of solution.

This happens when the 'oily' essential oils can't stay dissolved in the increasing polarity of the solute. This is what we'd call a suspension (solid in liquid) or emulsion (liquid in liquid).