I dont know much of anything about the history between these two nations. I understand there was a hostage crisis in the '80s that didnt go very well for anyone, and that the Iranian government today is run by religious figures.
I feel like I get conflicting messages though, where on one hand I see the government as zealots who want to start a nuclear war, and on the other I see the people of Iran as basically not being that different from Americans (particularly the youth culture).
Why is it that we in the west have so much fear and distrust in Iran, such that we try constantly to limit their influence?
One of the earliest reasons for Iranian dissatisfaction to the US (and UK) was the latter's role in a 1953 coup d'etat.
The Iranian prime minister Mossaddegh had privatised the Iranian oilfields. Iran at the time was a democracy and it's Prime Minister was popularly elected. The US and UK conspired to topple the Iran regime and reverse the privatisation. The result of the coup turned Iran in an absolute Monarchy.
More recently, US support for Iraq, including weapons sales to Saddam Hussein during the bloody Iran-Iraq war in the 1980s has fuelled their dislike for America.