This is the original photo without any grunge effect.

And this is after adding grunge effect.

Step 1:
Open your picture in Adobe Photoshop (File >> Open).

Step 2:
Navigate to: Filter >> Artistic >> Fresco

Apply following effect.

After applying fresco effect, our image will look like this:

Step 3:
Create a new layer by clicking “new layer” shortcut icon.

Step 4:
Now we will add some grunge brush on the image. Download Grunge_Brushes_005_by_Tackybrush from here. Extract the zip file and load the brush. I download this brush from here.

Set opacity to 50%. Now use different gray color and grunge brush and apply on the images many times. Here is final image.