Fiscal policy is the use of taxation and government spending to achieve macroeconomic objectives. Expansionary fiscal policies such as cuts in income tax will increase the disposable income of consumers, increasing consumption which is a component of aggregate demand (C). This will lead to a right shift in the AD curve, and alleviates a recession as GDP increases to its natural rate. However, the effectiveness of this policy depends on the marginal propensity to consume of citizens, as if its very low a tax cut will not initiate much added consumption.
Another way the government could counteract a recession using fiscal policy will be the use of government spending to stimulate demand. The government could increase spending on infrastructure projects. This will boost AD as they will hire workers which will spend their disposable incomes, boosting the economy by more than the initial spending. This is called the multiplier effect, and will increase GDP alleviating a recession. However, this also depends on the marginal propensity to spend, as if consumers don't spend their disposable incomes the multiplier effect will be negative. Also, a negative effect of increased government spending is the budget deficit associated with it, which cannot be sustained indefinitely, and will eventually have to be paid back, potentially by future generations.