The two major examples of expansionary fiscal policy are tax cuts and increased government spending. Both of these policies increase aggregate demand while contributing to deficits or drawing down of budget surpluses. They are typically employed during recessions or amid fears of one.
Classical macroeconomics considers fiscal policy to be an effective strategy for the government to counterbalance the natural depression in spending and economic activity that takes place during a recession. As business conditions deteriorate, consumers and businesses cut back on spending and investments.
Individual Response to Recession Can Make It Worse
This rational response on an individual level can exacerbate the situation for the broader economy. The reduction in spending and economic activity leads to less revenue for businesses, which leads to greater unemployment and even less spending and economic activity. During the Great Depression, John Maynard Keynes was the first to identify this self-reinforcing negative cycle in his "General Theory of Employment, Interest, and Money," and identified fiscal policy as a way to smooth out and prevent these tendencies of the business cycle.
How the Government Stimulates Spending
The government attempts to bridge the reduction in demand by giving a windfall to citizens via a tax cut or an increase in government spending, which creates jobs and alleviates unemployment. An example of such an effort is the Economic Stimulus Act of 2008, in which the government attempted to boost the economy by sending taxpayers $600 or $1,200 depending on their marital status and number of dependents. The total cost was $152 billion. Tax cuts are favored by conservatives for effective expansionary fiscal policy, as they have less faith in the government and more faith in markets.
Liberals tend to be more confident in the ability of the government to spend judiciously and are more inclined towards government spending as a means of expansionary fiscal policy. An example of government spending as expansionary fiscal policy is the American Recovery and Reinvestment Act of 2009. This effort was taken on in the midst of the Great Recession and totaled $831 billion. Most of this spending targeted infrastructure, education and extension of unemployment benefits.
(For related reading, see: How Tax Cuts Stimulate the Economy.)