When a family member dies certain formalities must be dealt with first. These include finding the will, contacting the executors if they are unaware of the death, and then arranging the funeral.
The funeral director will deal with many technical issues and be able to answer most of your questions, therefore you need not worry about formalities that you do not understand. For example, if it is necessary for the body to be sent overseas and for permission to be obtained from health authorities, this will be dealt with by the funeral director.
The executor of the deceased's will has the legal right and obligation to arrange the funeral.
The deceased may have expressed wishes about arrangements for the funeral, either in a will or a letter of last instruction, such as whether he or she wished to be buried or cremated, and whether or not there is to be a religious service. The executor is not legally bound to follow these instructions, but it would be unusual for them not be followed.
Funeral expenses (including any shortfall if the deceased arranged and paid for the funeral in advance) are generally met by the deceased's estate (his or her assets).
If there is no money available for the funeral you should contact Work and Income New Zealand immediately to see if a grant is available for the funeral.