What happens once a deceased person's eye is removed? how do they give it to someone else?

The transplant team: notified, and places all corneas and other organs that are donated on ice to keep it viable for the patients who will be needing it from the transplant bank. It's done sterile in the OR, and quickly, as soon as the person has passed. Then, when the tissue is needed for transplanting this is all coordinated beforehand so it's available when the corneal transplant surgery takes place.