Holders of a New Zealand passport do not need to obtain a visa to enter Denmark as tourists. On arrival they will be issued a tourist visa that allows the holder to stay in Denmark for up to three months.

Anyone visiting Denmark for short periods of time from a country with a visa requirement for entering Denmark must obtain a visa before arriving there.

A visa normally grants the holder a right to stay in the entire Schengen region: Belgium, France, Greece, Iceland, Italy, Luxembourg, Holland, Portugal, Germany, Spain, Austria, Denmark, Finland, Norway and Sweden.

A tourist visa does not grant the holder the right to work in Denmark

Visit Danish Immigration Service website for more information.
http://www.nyidanmark.dk/en-us/frontpage.htm