How in the world did China go from being a weak nation after World War II to becoming a superpower within 50-60 years?

After WWII, China had some of the same advantages that the US had and some unique to China. The relatively unscathed US just recovered faster and earlier.

1. It was isolated by the vast Siberian winter lands to the north and the impassable Himalayan mountain ranges to the west and surrounded by the Pacific to the east and south. Besides the self-inflicted damage during the reign of Mao, China was not under threat again.
2. It had the largest population on earth, with a large percentage of youth as WWII killed off the older generation. The demographic backdrop should not be underestimated. However, the misguided one-child policy has reversed those trends for at least several generations.
3. It had tremendous untapped resources at its disposal. For millennia, China had operated as an advanced and self-contained country as it had everything it needed from gunpowder to silk. For a rapidly industrializing country, China could tap into its vast coal resources.
4. It has some of the deepest cultural roots in the world, going back 5000–8000 years, with a heavy Confucian emphasis on education, obedience, and respect. That led to generations of the hardest working people on earth, trying to dig themselves out of misery.

With those ingredients, all that was needed was an unshackling of the natural competitive drive of the people. When the current communist party started liberalizing the control of the economy in the 1980s, China was still a third world country. But, through application of ingenuity and a no-holds-barred attitude towards hard work, the Chinese were able to capitalize on the consumer culture around the world, especially the US. This led to the greatest transfer of national wealth next to Middle East oil.

As for China becoming a world superpower, I would say it's still not quite there. The Chinese have been quite shameless in copying intellectual property and military intelligence to make up for lost decades. As many eager Western companies have learned in their partnerships to develop business in China, the trade-off between opportunity and loss of critical business intelligence hasn't been good. After a few years, the Western partners are often forced out of the joint-ventures, leaving the Chinese partner holding on to the golden goose.

Similarly, the Chinese have copied or reverse engineered key military equipment like fighter jets, saving hundreds of billions in research and development. Of course, that means China will always be one-step behind and in military terms, that prevents them from being a true superpower.

In the last 30 years, some of the above advantages have been exhausted. The population is still the largest but it's no longer young. The burden of social services for the elderly who built the current economy is just starting to crush the economy. All the monetary stimulus in the world can't overcome that. The vast resources have been drained quickly. Beijing is out of fresh ground water and clean air. Food is increasingly becoming polluted or otherwise adulterated. For the younger population, many have become disaffected by the dimming prospects of a brighter future due to hard work and continued growth.

Essentially, China is becoming like a giant version of Japan, about 11 times the size in population, with a similarly shrinking and aging population. Unlevered growth in China has slowed to a crawl and maybe reversing. Even with some of the highest central debt levels in the world, growth is slowing fast. China can easily see itself succumbing to the same stagnation as Japan in the next 30 years.

Source quora.com