Depending on what shades you want to bring out in your eyes you can go with a variety of shadow colors. Greens will make your eyes appear more auburn and/or chocolate while purple will bring out the gold in brown eyes. Blues are also a complimenting color and will bring out the amber in brown eyes.
You can incorporate these into your eyeshadow colors or try using an eyeliner in one of these shades.
Hair color can also play a small role in choosing colors so if you have a hair color that can clash you will want to make sure to choose something that will go with eye color and hair color. I recently put more red in my hair and now I tend to use more rust colors and gold to bring out my brown eyes. I can also do green and purple but have to me more careful with blue shades.
Have fun exploring your new looks!