You can generally stop hyperinflation in very similar way as any inflation. It is generally accepted by economic profession that price level $P$ (change in which is by definition inflation) in an economy is determined by money market equilibrium. In turn a simplified model of money market equilibrium can be given by the following equation of exchange (see Mankiw; Principles of Macroeconomics pp 87):
$$P= MV/Y $$
where $M$ is the money supply, $V$ velocity of money (i.e. how much one unit of currency is used on average) and $Y$ real output (also note this is a simplified version - more complex ones depend also on expectations of these quantities, but given that you are non-economist I think it is better to stick to this simple one - in case you would be really interested in the more complex versions Romer Advanced Macroeconomics is a leading macro handbook).
Next, hyperinflation does not have exact definition, but typically people consider inflation higher than $50\%-100\%$ per month a hyperinflation (e.g. see Sachs, 1987). Consequently, to stop hyperinflation you just need to make sure that the (expected) change in the right hand side $\Delta(MV/Y)$ is less than $50\%$ per month.
Government issuing its own fiat currency has complete control over $M$ so one option would to decrease the rate at which new money is created. Government can also to a certain degree affect velocity of money $V$ since it does depend on nominal interest rate (increasing nominal interest rates will lower $V$). In addition government has also some control over real output to the extend it can make some structural reforms that help economy grow or various policies that can expand $Y$. In addition as mentioned in the second paragraph this model is simplification and in real life expectations matter as well. This is why often countries that try to combat hyperinflation resort to monetary reform where they replace their currency with new one (this is meant to signal to the public government is serious about the issue thereby lowering their inflation expectation). Naturally, some combination of the above is always an option. Of course, this is just very broad and brief explanation. One could write whole tome on this issue, but exhaustive review would be too long for SE (for more in depth treatment you can have look at above mentioned Romer and Mankiw textbooks as well as Sachs (1987, Kiguel (1989), Reinhart & Savastano (2003) - in addition Cagan (1989) has whole book on hyperinflation - and sources cited therein).
Regarding whether there are any benefits of hyperinflation, there are generally only very few. One big benefit is that it can help country to inflate away public debt. Also, hyperinflation actually does not help economy to grow. Regular inflation can help economy grow, but when it comes to hyperinflation, it is generally agreed that its effect on output is on net negative as any benefit that it has in terms of boosting export through exchange rate, or through removing nominal friction are smaller than the negative effects on output which are caused by uncertainty it creates, and due to other costs of inflation, as well as due to the fact that hyperinflation often leads to people abandoning the currency altogether, in worst cases resorting to barter which is very inefficient form of exchange (see the sources recommended in previous paragraph for discussion on this).