Just like the rest of your face, cleansing around your eyes is extremely important. Especially because it tends to dry up very easily. Removing excess make-up from around your eyes will also ensure that it remains clean. Put some cleanser on a cotton pad and lightly set it on your eyelid. Gently swipe it off.
Not only external care is required for your eyes, but internal as well. Make sure that you are taking vitamin A, B, C, D and E supplements so that not only the skin around your eyes, but also your eyes in general is taken care of.
Getting 7 hours of sleep is extremely important. Make sure that you do not compromise on this point. Sleep will ensure that you do not get dark circles and wrinkles around the area.