How do you treat a paper cut on your eye?

Ointment. Refresh pm, systane ointment, or genteal gel applied to inside of lower lid can help healing.
Pain control. Paper cuts to the cornea (a corneal abrasion) can be very painful, depending on the severity of the cut. Infections are also a concern. Try to keep the eyelid closed as much as possible and use otc pain meds. If there is no improvement within 24hrs. Or if there is a goopy discharge, see your physician or ophthalmologist for definitive care.