Flying from New Zealand — México
There are no non-stop flights from New Zealand to México. Just like from Australia, the cheapest single-stop routes usually connect through Los Angeles: from Auckland try American Airlines, Air New Zealand, Continental, Delta, Qantas, and United. From Los Angeles, many airlines connect to numerous destinations in México. (For more information on getting to México from the US, read the article "Flying from the US.")
Alternate routes run through South America. From Auckland, LAN and Qantas both fly non-stop to Santiago and Aerolíneas Argentinas flies non-stop to Buenos Aires. (For more information on getting to México from Latin America, read the article "Flying from Latin America.")
Even though there doesn't seem to be much variation in prices, the peak travel times from the southern hemisphere to México are the summer months of June and July and the winter months of December and January.
A quick way to figure out carrier, route, and fare options is to check a few of the New Zealand-focused travel search websites such as www.travelocity.co.nz and www.expedia.co.nz.