You should contact a funeral director as soon as possible after the death, they will be able to guide you though the legalities and advise you on what to do next. The death will need to be registered as soon as possible, however, in some circumstances you may not need to register the death before the funeral.
The Patients Affairs Office at the hospital may be the first people you have contact with. They will be able to advise you on the next steps. If your loved one did not die in hospital it is best to contact a Funeral Director as early as possible.
Link through to the Who needs to know page for more info.