How do the U.S. Government and the Federal Reserve counteract the severity of a recession?

Answer 1

If past practice means anything, they wait for it to end, and then take credit for ending it.

Answer 2

Through Fiscal and monetary policy.

Fiscal policy is the job of congress and the president. This could mean more deficit spending, job training, and/or tax cuts.

Monetary policy is the job of the Federal Reserve. They would act to stimulate the economy through lower interest rates, and more money in the economy.