You can make the following types of changes through the 'Manage a Booking' section on emirates.com:
General booking changes:
If you need to make other changes, please contact your local Emirates office. Please note that if you need to make changes to a booking that includes travel on another airline, you may need to contact the other airline. If you booked with a travel agent, please contact them directly to make changes.
There may be a fee associated with making changes to your booking depending on the fare conditions of your ticket.