St0ven has a tutorial about dithering
here, not sure if it covers all the aspects but I guess good as an introduction.
I dont think dithering is a pixel style but more like a technique to apply in pixel art. Ideally you should use it for applying texture, saving color count, adding different effects, and for stylistic purposes, though the last one is more of a "each to his own" matter (and I believe it shouldnt be abused, and it working better if it aint the only technique you use).
What you did with your picture doesnt really work. Sure it is dithering but doesnt help the picture, it's just there randomly sitting making the picture look rather jagged. The palette you used has colors so close that dithering aint even needed, actually it is almost unnoticeable unless you zoom.
You could go to this thread
http://www.wayofthepixel.net/pixelation/index.php?topic=932.0 and look at some of the pictures posted there and see how they use dithering.
Not meaning to sound harsh, but if you are going to use it wrong, I believe it's better not to use it. Then again you could practice if you are willing to "master" it.
Good luck with further stuff