For many of us, that means looking for passenger lists of the 19th or early 20th centuries. The problem for the new researcher (and sometimes the more experienced with a brick wall) is that there is no one-stop shop for this information - it is scattered amongst a range of sources, some on the Internet and some not; some in NZ and some overseas; some in published hard copy, but most not. Knowing where to look, and what to look for, is quite a task. So today I want to discuss some of the best resources that I know of as a librarian, in the hopes that they may help someone make that new discovery or breakthrough.
A list of sources on this complex situation, can be found amongst the research guides available on the website of Archives New Zealand.
On a first look-through, the list of possible sources seems a bit overwhelming, particularly if you only have a vague idea of when and where your family first showed up in New Zealand. So, the key is to work on that question of "when and where" till you have as accurate an idea as you can of the answer.
Look at electoral rolls, post office directories, and records of birth, death and marriage, to establish a timeline and location. Once you know that, check to see what resources exist for the nearest port, in the time period they first appear. As a rule of thumb, it is best to assume that people settled somewhere in the vicinity of their port of first entrance to NZ. This of course was not always the case, but it happened frequently, so start with that assumption till proven otherwise.
Examples of these are AUCKLAND , TARANAKI , WELLINGTON ,CHRISTCHURCH , and NELSON.
WARNING. It is always tempting to just jump in when searching a newly-found database, but you are not helping your research efforts at all if you don't also read about what it contains (or doesn't!) and how it is arranged. You may be missing some vital piece of information and not getting a hit on your search because you didn't know some fact that was explained in the introduction to that database which you skipped in your excitement. BE SMART AND READ THE NOTES.
Many official passenger lists are held by the government department called Archives New Zealand. Previously only accessible through (Wellington-based) card indexes, these are now being digitised in a joint project with the Latter Day Saints' FamilySearch.org. This is an ongoing project so you may need to keep checking for your family names till you get a hit, but when you do, you will be able to obtain (without charge) an image of the original passenger list. See a similar joint project that operates between The National Archives UK and the commercial site Findmypast is 'Ancestorsonboard' which traces passengers leaving UK ports for all destinations (NZ included) from 1890 to 1960. It can be searched for free on the Internet but copies of the transcribed results or images of the original passenger lists must be purchased.
The Central Auckland Research Centre has a subscription to this database which visitors may book and use to either do a search from scratch, or, if they already have done the free part of the search online, to obtain the image of the passenger list via our subscription access without further charge, if a memory stick is used, or standard photocopying costs if a paper printout is made. (Note, the colour versions although a dollar for an A4 page, often look much better than the cheaper black and white). Bookings for access to this are required as the number of people who can use the subscription at one time is limited.
Last word. If you still can't find that elusive record, do not despair. More and more material is being made available on the Internet as time goes by. That breakthrough may be just around the corner!
Another
It started with Shelley from 

