More specifically, things like how were warriors selected for a particular war party? How were supplies handled? Obviously Maori war parties were much smaller than European or Asian armies, moving over smaller distances, but they were still people, who needed food, water, and shelter.
First of all, we'll need to sort out some basic terms and their definitions to make this understandable, otherwise it's going to be a whole heap of confusion for all the non-Kiwis on this sub.
Iwi - A tribal group. The largest group.
Hapu - sub-tribe. The next level down from iwi. Described as "the primary political unit in traditional Māori society", a hapu was descended from a common ancestor, and multiple hapu formed the iwi, which was a far looser connection.
Utu - to repay or respond. Often mistranslated as revenge, it was used for this purpose, but could also be a positive trade such as repaying a favour. Utu was the main reason for all Māori warfare.
Mana - Prestige, authority, power. This one's harder to translate into English, as I don't think there's any word that really does it justice. It's something that commands respect. I feel like any of the three words I gave would do it, but qualified with "dignified".
So with those basics down, we move on to the makeup of a war party. These were known as taua, and they were made up of the men of the hapu who were going to war. Why would a hapu go to war? And why would all the men of a hapu go? Māori weren't professional soldiers. They didn't sign up to the army and spend all their time training. They were hunters, fishermen, farmers, etc. When a hapu went to war, it was because of utu. Most often, it was the way that a grievance could be balanced out through utu, usually with a gain of mana for the victor. An insult or diminishing of the mana of one man also affected his hapu. As well as that, a hapu were tightly knit, unlike the iwi. This meant that when insult was given, the whole group went together. So if you were a member of that hapu, you were in if you were fit to fight. This is further backed up by the fact that in peacetime(which was a lot of the time), the main focus of a Māori community was on growing food and maintaining homes, pa(fortresses), and waka(canoes). The importance of the waka and the pa in Māori military operations suggests that rather than warfare being a natural state for Māori, the natural state was in actuality being ready for war, or actively discouraging it by being ready.
Māori warfare wasn't supposed to kill the entire enemy taua. Weapons(pre-European arrival), were hand to hand only, and generally, only a few of the fighters would die from each side. Remember that hapu were the units in which wars were fought, and that they could number up to around 500 per sub tribe. This was vastly different to European warfare where tens of thousands of men could be involved.
As for your logistical query, it wasn't much of a problem. With the smaller scale of the battles, not as much food was required. Some was taken with them, but generally portable food was uncommon and the battles were quick, so it was unneeded. In times where it was, this website says that some women and older children would accompany the taua to provide water and food. I'm not sure of the veracity, but it doesn't seem unlikely. Another quote I saw in King's History of New Zealand mentions that women and children were not given any more mercy than men in a battle, so their presence is likely, although I can't say with certainty whether that refers to their presence in the pa or not.
Hope this helps!
Sources:
The Penguin History of New Zealand by Michael King. It's on the booklist for more details.
Huia Histories of Māori ed. by Danny Keenan. Also on the booklist.