The federal reserve can manipulate the economy using the fiscal policy. The tools that it uses are interest rates and money supply.
In times of recession the federal reserve generally lowers the interest rates which stimulates the economy by allowing firms to borrow money at a cheaper price. Also, the consumers are encouraged to spend more. This leads to increase in production output and hence increase in employment rates.
To control the inflation, feds increases the interest rates, which decreases consumer spending and allow them to save more. Higher interest rates mean higher price of borrowing and therefore, inflation level decreases.