I'm not an expert on China at all, so half of statements here are assumptions, but I'll try to start.

First the official story about how China became economic powerhouse and pretended to world leadership.

After Mao period with hardcore stalinism and local craziness like Cultural Revolution with destruction of everything or killing sparrows because they are pests, China was in pretty bad economical condition. Government even had no proper statistics about economics, local government official were corrupted and selfish as always, there were food shortage and overall goods deficit - typical for planned economies.

Deng Xiaoping and his political group took control of Communist party, replacing old Mao faction, and started to do economic reforms, program called "reforms and openness". First they took agricultural sector. In 1978-1984 government replaced communes and brigades in agriculture with formally private plots of lands for families and local collectives.

In all parts of economics there was process of decentralization, local management got more freedom, private-like enterprises were allowed in some form. There still was a planned process with mix of fixed and market prices, different types of control from state and other thing, but overall economy moved from planned socialism to state capitalism. Foreign investment was supported, free economic zones were created.

Economy became more market in 1990, when system slowly transformed from plan-market mix to market with heavy government control, without noticeable plan part. Even typical capitalist traits are emerged, like income inequality and liquidation of inefficient, but important factories (that is always a heavy hit to local population).

Yet growth was tremendous. China transformed from mostly agrarian state with ruined economy to industrial and scientific leader. While in 80-90s it was just an outsourcing that was loved by everyone by cheap labor and low bureaucratic restrictions, now it is independent and self-sufficient country that actually competes with "old leaders" even in innovation. And even considering income inequality and some social problems, average Chinese now lives much better than in past. It is hard to compare average numbers like GDP per capita or wage, because China is too large, but there are plenty of places where average wage is already about 1000$. Different sources say that population already have income comparable with EU periphery.

https://en.wikipedia.org/wiki/Chinese_economic_reform

Actually, it would be better to see someone with Chinese background to discuss this, because China is pretty "closed" to outsiders, but has large amount of historical materials and cultural things that we don't know.