I would identify three main aspects of the new conservatism that was manifested in Ronald Reagan's presidency.
First, there was anti-communism. Reagan stood strongly against what he called the "evil empire." He was willing to do whatever he thought best to fight communism.
Second, there was the idea of "smaller government." Reagan argued that government was the problem with America rather than the solution. He argued for a need to reduce the size of the government.
Finally, there was cultural conservatism. This was based on things like opposition to abortion and unhappiness with the new cultural values that had come out of the 1960s and 1970s.
These three issues formed the basis for the new conservatism of the '80s.