Yes, Deng was exiled from politics during the cultural revolution (he was sent to work as a common factory laborer) and was allowed back into a position of power by Mao because he realized that the PRC was a mess after the cultural revolution. He also realized Deng was one of the few officials left who had the calibre to repair the country after he (Mao) died.

Deng emerged out of the post-Mao power struggle as the undisputed ruler of China after 1979, defeating Mao's intended successor Hua guofeng. Deng sent many expeditions to tour the west and he himself famously visited Paris where he had worked as a common factory worker in the 1920s. Every tour of the west revealed to Deng and the party just how far behind China was in terms of industry, technology and agriculture. Radical reforms was required and China must learn from the more advanced nations.

The first big reform came in agriculture when the government, with Dengs support, at a stroke decollectivized agriculture. Under mao almost all farming was done in large communes composed of thousands of people. They were often inefficient to the point of threatening a famine in the Anhui province in the late 1970s. Deng supported the establishment of the household responsibility system under which each family would farm its own land, hand in a set amount of crops to the state and be allowed to sell the surplus for profit at market prices. As a result of increased incentives and technological breakthroughs of the Chinese green revolution agricultural yields shot up to levels unseen in the Maoist era.

In terms of industry, Deng supported the establishment of small scale rural industries producing consumer goods called TVE (town-village enterprise). They were ambiguously public-private partnerships which tapped into China's cheap rural labor to produce goods for both domestic and foreign consumption. This stood in contrast with Maoist focus on heavy industrial goods like steel produced in urban areas by privileged state workers. He also initiated the creation of special economic zones (SEZ), in which far greater "capitalism" was allowed than the rest of the country as to allow China to have area of capitalism without destabilizing the rest of the country with rapid changes. The most famous example of this is the city of shenzen, which was almost entirely built during the Dengist era. This laid the foundation for China to become the industrial powerhouse it is today.

Deng also reformed the pricing system in the country. Under Mao, the government fixed prices of goods. Therefore a true market cannot exist and it is difficult to determine the value of a good through prices. Deng understood that this needed to change but inflation must also be avoided. So the government established the dual-pricing system, under which the state sells a certain amount of goods at fixed prices to ensure the population can afford basic goods, but any "excess" goods would be sold at market prices. This system was ultimately of questionable effectiveness due to arbitrage between fixed and market rates by corrupt officials and inflation by the late 80s hit 25% per annum in Beijing. This contributed to the tianenman square incident.

I do not discuss privatization because there was a limited amount of it during the Deng era. Deng likely was conscious that privatizing state assets would anger members of the party and therefore thought it best to wait until reforms bore fruit to push through politically unpopular measures.

This is of course, a superficial look at Chinese reforms during the Deng era, but Deng did establish the foundations of a capitalist economy in china. His efforts would be continued by premier zhu rongji in the 1990s. Deng's accomplishment was to turn back on Mao's radicalism, find something which worked and call it socialism with Chinese characteristics.