Flying from Asia — México
To our knowledge, the only non-stop flights from Asia to México are Aeroméxico's from Tokyo and Shanghai to México City. Although not non-stop, Japan Airlines has a direct flight from Tokyo to México City that stops briefly in Vancouver.
Otherwise, from Asia, just like from Australia and New Zealand, the cheapest single-stop routes usually connect through west coast cities in the US and Canada. From there, many airlines connect to numerous destinations in México. (For more information on getting to México from the US and Canada, read the articles "Flying from the US" and "Flying from Canada.")
From western Asia, going west, via Europe, is an option.
A quick way to figure out carrier, route, and fare options is to check a few of the travel search websites such as www.expedia.com and www.zuji.com (a Travelocity owned site that focuses on travel to, from, and in Asia).