How to derive the intensity from two emitters?

In a comment at How come unpolarized light does not undergo destructive interference? hsinghal said the following:

A light source is made of larger number of small light emitters. In order to get the intensity you have to add the field amplitude from each one of them. Let us say you add field of two emitters you will get $I=I_1+I_2+2\,I_1\,I_2\,cos(\Phi)$ . $

Exactly what is intensity and how do we derive that equation? I can accept a trig identity without derivation, but I need help getting to the point where we need the trig identity.