How do i apply for the medicare scheme?

It's pretty easy, just print out the form here: http://www.medicareaustralia.gov.au/public/files/ma_3101_medicare_enrolment_application_form_011005.pdf
Make sure you check the first section to make sure you are eligible and then take it into a Medicare office with your ID to get your card.

go to the nearest medicare office in the area u are planning to live.. take your newzeland passport with you if u are a newzeland resident you will get 1 year medicare.. for newzeland passport holders it for 5 years and after 5 years again renew it.. nz citizens and aust citizens will be treated as same for medicare.. so you need not worry.. forms can be filled at medicare office. they will give you there