I call what I typically do for eye shadow application a "layered application." There might be a real term for that I don't know. ;)
I of course start off by applying primer over my eyelids but what do I do next?
Here's the very basic application:
I first apply a medium color on the eyelid. This will really be the main color that will be visible and that will indicate what the color of your makeup scheme is. I apply this color all over the eyelid, from the lash line to the crease.
I apply a darker and/or contrasting color at the crease. The area that will be covered is from the outer corner of the eye towards the side of the nose (without touching the side of the nose). You can bring it down towards the inner corner of the eye as well but it may give the illusion of closing your eye (i.e., making it look smaller) so we generally keep the application higher.
On the brow bone, I apply a light color. This is really an optional step but it does make the eye look appear more finished that way... and it gives a little highlight/brightness to the eye. This step is especially important if the colors on the eyelid and at the crease were on the dark side.
Arch of the eyebrow
I sometimes will apply some white or other shimmery color at the arch of the eyebrow. This will further highlight the eye area. If you've already used some very pale color on the brow bone, you won't need to do this but, if not, it could be another way to brighten it all up.
Lower lash line
This is another optional step, which is to apply eye shadows at the lower lash line as well. I like to do this as it makes the eye look more finished, imho. When you're applying eye shadows there, though, you want to use a very light touch because it's super easy for the bristles and shadow to go in your eye... which is not fun, believe me. I generally repeat the same colors on the lower lash line in the following fashion:
1. I apply the eyelid color all over the lower lash line (that way there won't be a gap).
2. I apply the crease color at the outer corner of the lower lash line and bring it up in the crease. That's how I flare my crease application.
3. I sometimes will apply the brow bone color at the inner corner of the eye, blending it in the inner corner of the lower lash line. This further opens your eye area.
Note that I generally will apply the color after I'm done with the original area that I applied it on. That is, I apply the color on the eyelid then on the lower lash line; then the other color at the crease and the lower lash line; etc.
Another option with the lower lash line is to use a contrasting color. This can easily brighten or darken your makeup scheme so you'll want to try the idea beforehand or risk not having the exact scheme that you thought you'd have.