Escorting the body
If you want to escort the body (that is, fly on the same plane as the body to the destination), tell the funeral director you're working with so that he or she can help you coordinate your travel. The funeral home or airline will be able to let you know what flight the body will be transported on, and you'll be able to purchase a ticket on that flight.
Collecting the body
Even if you escort the body, the funeral home may still pick up the body at the airport (either as a service to you or because of legal body transportation requirements of the state).
If you escort the body on the plane and want to transport the body yourself once you reach your destination, you'll need to check the laws around body transportation at your destination. If you are allowed to transport the body yourself, you will retrieve the body at the luggage carousel rather than at the cargo terminal.