There is no a universally acknowledged theory about color matching. Generally speaking, colors will make different flavors when they go together. It is hard to judge which one is better as people have different taste. If you really care about it very much, I have some suggestions based on general aesthetics. Fist of all, if your eyes are pure green like the leaves in summer; don't go with dazzling colors like scarlet only if you want to look as festive as Christmas. Green is cool color. It will be good when it goes with other cool colors such as blue and grey. White and black are classical colors which could be perfect for any match. Additionally, light yellow is also an ever lasting match of green, it makes people feel fresh. The suggestions above are just based on idea of general. If you want to fashion, there are a lot of work you may do by yourself. Even it is hard for most people to accept red and green to go together, but some designer combines together to make a crash. That is also stylish.
There are lots of colors for clothes you can try. For example, you can try plums, mauves, pinks, rose-based browns and beiges clothes will make you amazing. Besides, you can also try emerald green clothes that will make your eyes pop. Anyway, you shall try to formal your own appreciation of beauty and wear your own style not just for match your eye color.
If you want to look refreshing and young, the white clothes may be suitable with your green eyes. The combination of white and green is perfect which will make you look great. If you want to look cool, you could choose the black color of clothes to match with your green eyes.