What was the US's role in helping the shah of Iran become the shah?

Answer 1

Assuming by "The Shah of Iran", you are specifically referring to "Shah Mohammed Reza Pahlavi" who is only the last in millenia-long line of Shahs, there are two times that he came to power (because he abdicated midway through his reign). Only the second of Mohammed's ascension to power involved the USA.

Coming to Power in 1940
In 1940, in the midst of World War II, Shah Reza Pahlavi (Mohammed's father) had a pro-German view, even though he remained neutral. This was unacceptable for both the UK and Soviet Union (USSR) which need Iran to serve as a corridor for troop passage and petroleum passage between British-controlled Iraq and the Soviet Union. As a result these two countries sponsored a coup to replace Reza Pahlavi with his son Mohammad Reza Pahlavi. The United States had nothing to do with this coup and had a profoundly isolationist stance at this point in history. Mohammed Reza Pahlavi remained in power until he abdicated in 1951 after facing strong hostility from the Iranian population.

Coming to Power in 1953
In 1953, the CIA launched a coup d'etat in Iran, called Operation Ajax. which re-installed the Shah of Iran after he had been forced out in 1951. The US and UK both knew that Iranian Prime Minister Mohammed Mosaddegh would nationalize the oil fields in Iran, which would have huge economic ramifications for the UK, and feared that he would create an alliance with the Soviet Union since he was very amenable to Iranian Communists and their political views. As a result, the US and UK both preferred the strongly Western-aligned Shah Mohammed Reza Pahlavi and instigated the coup that put him in power. The policy was negative, not only for the citizens of Iran who were subjected to numerous human rights abuses post-replacement, but also for the US which alienated the Iranian people in the long-term and was unable to seriously halt the growth of communism.