How does the government reverse hyperinflation?

By not printing more money which is the primary cause, stabilizing the economy, de-tendering older money and creating new money that can be exchanged at a large ratio... for instance, 1 Reichsmark for 1,000,000,000 Papiermarks.

Of course, now that "western" countries do so much of their financial transactions electronically and with credit, the printing of actual money is less directly related to inflation and the concept is more commonly used as a metaphor for the increase of the money supply thorough other mechanisms, some of which are not as directly controlled by the government as is the printing press.