How can I keep my eyes healthy with vitamins?

You can't. This doesn't mean you need to be taking vitamins; it means your eyes (and most other organ systems) won't function without them. For most vitamins (d is the exception), the best source is not a vitamin pill, but a really good diet. For good health, eyes included, eat lots of different fruits, vegetables, whole grains, etc. For eyes specifically, veggies with vitamin a are particularly helpful.
No proof. If one has a 'normal' diet, vitamin supplementation has not conclusively been shown to improve eye health. With certain vitamin deficiencies, such as vitamin a etc.. Supplementation would be helpful. The only vitamins shown to have beneficial effect are the so called - areds vitamins. These have been shown to slow macular degeneration in susceptible patients and may be recommended by your dr.