Milling lumber is not as easy, or simple, as you might think. If you're only going to do it once in a while, the most economical and simplest way is to hire someone with a portable mill. These people may not be prevalent where you live and in many large cities, they're pretty much non-existant (supply demand thing I guess). You'd probably have better luck finding someone to do tis in more rural areas.
So if you still want to mill your own lumber, here's a few things to consider.
1. If you're only going to do this occasionally, or if you're just starting out, a chainsaw mill is the way to go. Chainsaw mills waste a lot of wood (about 3/8" or 9 mm kerf) but band saw mills are expensive to build (and more expensive to buy), take a big time investment, are very large (compared to a chainsaw mill), and must be stored (you need a parking space sized spot).
2. To get decent boards, you need something to attach to your chainsaw. You can make something yourself in a weekend but you'll need access to at least a drill press. Some designs require welding equipment. Alternately, you could buy an attachment like this one: Lumber Mill Attachment
... but you'll also need a straight guide board, a way to support the guide board, and a way to hold the log your cutting. Also, an attachment like this does not clamp the chainsaw bar very well (i.e. it comes lose in 10-15 minutes) and if you're not very careful, you will immediately dull your chain when it hits the metal clamp.
3. The first couple of cuts with this type of an attachment are relatively easy and you can get a couple flitches (i.e. bark still on edges) from the center by cutting the log in half, then taking a slab off each half (kind of like quarter sawn) but as the log becomes smaller, it becomes more and more difficult to support the piece that's left.
4. Usually, the attachment above is used to cut square sides after a flat top surface is cut (look at the video here: Three sided cant
5. Flat sawing flitches is realatively easy with a "ladder" mill. This is the easiest, cheapest thing you can make yourself. You'll need to buy, or make an attachment. These webpages explain it well: "Ladder Chainsaw Mill"
. The homemade attachment, shown on these web pages, bolts to the chainsaw thru holes that were drilled in the bar (don't drill thru the tip like he did - you'll ruin the bar sprocket). You can buy (or make) an attachment that clamps to the bar too. Granberg makes the best ones I've seen: Granberg Small Log Alaskan Mill
. The Granberg website has an online store but I've found their products cheaper on other websites (e.g. Bailey's
). Shipping to New Zealand might be an issue.
6. For milling quarter sawn lumber yourself, the best info I've found on the web is here (it features a modified "Granberg Mini Mill"): Quartersawn Lumber With a Chainsaw
. I've just finished making an attachment like this using bed frame angle, which I don't recommend since it's really tough stuff to drill (use plain steel instead). I still have to build some stands (mine will be made of dimensional lumber).
7. You can always just hack up the logs by eye but you'll waste a lot of wood and then you'll have to flatten and square the resulting flitches, which will be flat sawn (by definition). There are ways to use a router to flatten boards, so this might be the way to go but you'll have to cut the boards thick enough to account for what you'll lose when you flatten them. This will add to the drying time which was already posted (i.e. 1 year per inch). Also, once the logs are small enought, you can finish up with your bandsaw.