With any color of eyes, I find it is always best to use the lightest shades on the inside of the lid and use the darker on the outside to give beautiful definition! Like shown in the photo.
For brown eyes, use lighter colors so that there is not too much dark because of your brown eyes. I found that whites and champagnes also make brown eyes look bigger. Here is a link for shadow that enhances brown eyes! http://www.ebay.com/itm/Physicians-Formula-Shimmer-Strips-Shadow-Liner-bronzed-brown-/271505082543?pt=US_Makeup_Eyes&hash=item3f36f6c8af
Here is a palette that is especially for green eyes! http://www.ebay.com/itm/Physicians-Formula-Shimmer-Strips-Eye-Enhancing-Shadow-Liner-2221-GREEN-Eyes-/161312283121?pt=US_Makeup_Eyes&hash=item258ef619f1
I hope you found this guide useful!