1) Start up the mission "End Of The Road - The Desert".
2) Get to the part where you are in the Arid Desert.
3) You will be tasked to kill your target.
4) There will be a grave nearby with a bone in it, note the location.
5) Go to the dead dog on the floor and pick up the bone next to it.
6) Place it next to the bone on the grave you looked at earlier.
7) Go to the grave with a cross and move the bone on it to the grave with the two other bones.
8) The screen will turn black and white and a woman will start talking for about thirty seconds.

Here is a video tutorial of the easter egg: