Despite a friendly relationship with Latvia, New Zealand does not have an embassy in the country. To get a New Zealand passport while in Latvia, Kiwis must go through the NZ embassy in Berlin, Germany. Their information can be found here.
Basic Entry: New Zealand is among many countries whose citizens may enter Latvia without a visa.
Extended Stay: If you wish to have an extended stay and do require a visa, the Ministry of Foreign Affairs of the Republic of Latvia is a good place to start.
You can find the process of requesting citizenship, as of 1 Oct. , 2013, on the Embassy of the Republic of Latvia to the United States of America website.
There was a major change in the citizenship process during 2013 which you can read about here.
In 2017 amendments to the changes effected in 2013 were made. Learn more.