More can always be said, but there's a whole bunch in our FAQ about Polynesian voyaging and expansion, much of it by u/b1uepenguin.

Not a historian, but I am post grad in Anthropology with a focus on the Pacific (I am at a New Zealand University).

The waka (double hulled or single hulled with outrigger canoes) that explored Polynesia did carry water with them in gourds, but also they would carry items like coconuts that contain water and they would often know there was an island in the general area they were looking. When sailing between known Islands they would make stops to gather more supplies. They would also gain water or fluids from the sea and bird life they could catch.

One thing to remember is that they were very proficiant sailers by the time they were exploring Micronesia, Melanesia and Polynesia. The waka that discovered and came to New Zealand have oral traditions told about them that often includes oral traditions of what provisions they had on board. These oral traditions like that of the Aotea waka as talked about in the Ngāti Ruanui book by Tony Sole talk of the places that stopped off at such as Rangitahua (Kermadec Islands).

Māori and indeed Polynesians, Micronesians and Melanesians sailed with experienced navigators on board who sailed using what we call a star compass (look up star compass by Mau Piailug), these navigators would have also had the skills in helping to locate birds, whales, fish, turtles etc which could be caught and eaten (not so much whales but you get my drift). So to them the sea is also like a garden, or in te reo Māori we say this is kai moana (sea food).

Sailing through the Pacific was still dangerous at times and there are stories of waka that were lost even though many still made it to New Zealand (see the book Ngā waka o Neherā by Jeff Evans). The journey to New Zealand is often said to be the most dangerous, but with the correct knowledge from a Navigator could still be done and today modern waka that are built to be like traditional waka such as the Haunui and Hokūleā can make these trips without navigational aides even today. Although they take on modern provisions they still fish and eat the sea life as a form of sustenance on these journeys.

As for other means of survival, some waka had special stones that allowed them to cook onboard, others had prayers and oral traditions that forbade cooking or even taking many provisions and so they relied only what they could catch. Navigators also often knew how to avoid issues such as storms, but double hulled waka could also ride out many storms and they often had cover such as small huts built on deck to take cover in.

To really understand just how amazing all of this was there are some documentaries available on you Tube of Mau Piailug https://youtu.be/9IF8jCLxyAA who was one of the last traditional navigators in the Pacific and he taught Polynesians how to navigate by the stars again enabling modern ocean going waka to re-create these amazing journeys. Navigation is more than just knowing how to get somewhere it is forming an identity that is based on the ocean and understanding bird life, sea life, weather, currents etc.

It's good to note there are many other debunked theories such as drift theory. But the generally accepted theory now is that of navigation. For movement across the pacific they would sail up wind then allow the return journey to easily bring them home. New Zealand is considered the last major land mass to be settled by Polynesians because it seemed to be associated with the most risk and a return back to to "Hawaiki" would have been difficult although not impossible as spoken of about the Horouta waka, who is said to have returned to Hawaiki for Kumara (sweet potato). Hawaiki is a zonw that includes places such as Society islands, Cook Islands, Tuamotu's etc. Many waka that came to New Zealand speak directly to arriving from there, from islands such as Ra'iatea (in French Polynesia).

There are many books that speak about these journeys such as the ones mentioned above but also those such as the Horouta book, Takitimu book, Te Arawa book and also books such as Ngā Mōteatea.

Apologies for any spelling, grammar or formatting errors, I am writing this from my phone. If you have interest beyond this the New Zealand Archaeological Association is a great source of further information.