You can make the following types of changes through the 'Manage a Booking' section on emirates.com:
General booking changes:
Upgrades on certain Skywards Saver tickets using Skywards Miles are only eligible for check-in reward upgrades during online check-in and airport check-in. Silver, Gold and Platinum members can also request an upgrade on board. You will be notified during the booking process whether a fare is eligible for an upgrade immediately following purchase or only during check-in .
If you need to make other changes, please contact your local Emirates office. If you have booked through a travel agent and have not yet started your journey, we recommend you contact your agent to make any changes.
There may be a fee associated with making changes to your booking depending on the fare conditions of your ticket.