What happens when the gov't prints money?

How does this process work? It begs simple observations like “Why don’t we print enough money so everyone will be rich” or “it seems it would just reduce the real value of wealth”, but neither of those could be completely true. I know there are strong reasons for controlling the money supply (e.g. how Volcker beat inflation). But the Fed controlling the money supply isn’t the same as printing more money. How does this work? What are the benefits and consequences?