If you want to work in New Zealand you must apply in advance for a Work Visa. The Work in New Zealand(external link) section of the New Zealand Immigration website contains comprehensive information about the options available including:
New Zealand - Slovakia Working Holiday Scheme
A reciprocal Working Holiday Scheme (WHS) between New Zealand and Slovakia opened in April 2012. The WHS allows Slovakians aged between 18 and 30 years to work or study during a holiday stay in New Zealand for up to 12 months. A total of 100 WHS places are offered to Slovakians per year. Places become available each year in April and are filled within a short period of time.