When it comes to green eyes, there are two rules.
If you want a dramatic, but catchy look, then the eyeshadows you opt for should be opposite to the ones from your iris. For a more soft look go with some shades from your color wheel.
Use black eyeliner for your upper lid and opt for a light tone of blue. For a more dazzling look, choose a glittering shade if your eyes are a lighter green.
Go for a pearly green to accentuate your eye color. If you decide to go with a smokey eye make up you don't need to put any eyeliner. The eyeshadows you will use are enough, especially if they are of pearly texture. Put mascara on both the upper and lower eyelashes. Read more on youne.