President Carter initially tried to reduced unemployment and the lagging economy by implementing government spending increases (a Keynesian approach, in the style of FDR). But the result was spiraling inflation. Carter then tried to control inflation. He promoted Paul Volcker to the chairmanship of the Federal Reserve, and Volcker sought to keep inflation in check by raising interest rates. This did bring the Consumer Price Index down, but it caused other complications and further recession, such as rising unemployment.
Reagan blamed the economic problems on the Democrats and their government spending programs. He made it his mission to reduce the size of government and to give tax cuts. His "trickle down" economic theory believed that giving tax cuts to those at the top would filter economic benefits (jobs, better wages) down to those on the lower end of society. It worked to an extent, but not long term. Reagan's successor as president, George H.W. Bush, served only one term in office because the economy fell into a bad state again in the early 1990s.