tl;dr There was no hyperinflation in Germany during or after World War 2. There was a degree of inflation which was dealt with by rationing basic consumer goods (starting even before the war), but no hyperinflation as seen in the case of 1923 Germany or Zimbabwe. This is mainly because Germany in and after World War 2 had rationing and price controls and a much more controlled economy than in 1923.
The connection of inflation, hyperinflation and government spending
To finance expenditure, governments theoretically have multiple choices (and traditionally employ a mixture of them). Among others: First, they can raise taxes and pay with the tax income. Second, they can issue bonds, which are basically loans to the government, sold to primarily banks. Governments promise to repay them and pay interest on them. Third, they can have the central bank issue more money to pay for government expenditure (unless they have an independent central bank as most Western countries do today). This what is referred to as ''print money'', but does, in modern economies, not typically involve literally priniting anything.
Inflation can arise - among other possible causes - from issuing quantities of money beyond the capacity of the economy. Specifically, if the quantity of money used to pay for goods exceeds the amount of goods, either the price of those goods will increase (as is the case with inflation) or some of the demand will not be served (as is the case with price controls and rationing). However, it is a bit more complicated since the money supply is not identical to the quantity of money used to pay for goods. The economy may have a lot of money without actually trying to use it for things that are not there. Among other things, this depends crucially on whether people believe in the stability of the currency. If they suddenly do not, they will - frantically - try to get their savings into alternative forms of investments. In such cases, demand for money (people wanting to sell something else for money) erodes to zero while supply of money (people wanting to buy something else for money in order to get rid of it) skyrockets. With this, the value of money collapses as well. Once an economy reaches this point, it is very difficult to recover from this situation; in most cases only a currency reform (in order to restore confidence) helps.
Hyperinflation in Germany after World War 1
Germany ran a huge deficit during World War 1, which was mainly paid for by government bonds that would be due after the war. As long as victory seemed conceivable, and with it the possibility that the France or Russia or whoever might pay war reparations to Germany, these bonds seemed like a sensible (and patriotic) investment. Germany also ran a deficit after the war, caused by the collapse of the war economy, unemployment, social turmoil, and reparations Germany had to pay to other countries. Only this time, the case for buying government bonds was a lot less convincing; so they needed to find an alternative way to pay for this. They increased the money supply, they kept doing this beyond the capacity of the economy, confidence in the currency collapsed, and you get the inflation scenario described above. Instead of instituting a currency reform, they kept increasing the money supply to pay for domestic expenditure for some time; this was the driver of hyperinflation. After allowing this to go on for some time, they resolved the issue nicely with a currency reform.
Note that while this also eroded confidence in the government and the German economy and led to poverty and to social turmoil, it solved at least one problem for the government: Wartime bonds from the first world war were not an issue any more since they were officially worth practically nothing now. Also note that the government was under a lot of pressure internationally (French and Belgian troops occupied the Ruhr area when they temporarily ceased payments of war reparations) and domestically and may not have had any other choice than letting the hyperinflation take its course before they were able to resolve it.
No hyperinflation in Germany after World War 2
The economy of Nazi Germany was based on a Ponzi scheme. They again issued bonds, MEFO bills that were ostensibly bonds raised for a private entity ("Metallurgical research association") that never existed. This helped the government run a huge deficit to build up armaments for the upcoming war, while all this being off the record and under the radar of the international community. The effort was scheduled as a 4-year plan with the first bonds becoming due in 1938. The aggression against Czechoslovakia in 1938 was intended as the start of the war; it surprised the hell out of Hitler and everyone else that the international community simply allowed this to happen. The failure of the international community to respond allowed the German army some more time to prepare for the war, but it also brought the German economy to the brink of collapse, since, of course, they could not pay for the bonds that became due. The central bank president resigned and the bond holders were kind of forced to exchange the MEFO bonds against government bonds. In August 1939, they nevertheless saw the need to ration basic consumer goods. Note that this was before the start of the war and the invasion of Poland. Also note that this is the other possible way to react to an oversupply of money besides allowing inflation to happen (see above).
They were able to do this, since German society and economy was completely under their control by then. During the war, they further transformed the economy into what was practically a centrally planned economy similar to the ones in the Soviet Union and the east block states, even though it was privately owned and the individual firms were privately managed under government supervision. This economic system, labeled command capitalism allowed the Nazis to transform the economy completely into a war economy. Slave labor (war prisoners, concentration camp inmates, civilians from occupied countries) and what was pillaged from occupied countries (machinery, money reserves, raw materials at extremely low prices etc etc etc) was brought in as the economic needs of the war effort gradually increased. This intensified especially after the failure of the Blitzkrieg against the Soviet Union and after the US entered the war.
After the end of the war, the currency predictably collapsed. Since rationing remained in effect, the collapse did not lead to hyperinflation in the same way it did in 1923. However, the black market in Germany immediately after the war used (American) cigarettes as money, not the official currency. The following currency reform in West Germany had socialist characteristics (with small amounts per capita being exchanged 1:1, funds beyond a certain threshold being frozen and later cut by 70%) and was supported by massive financial support from the US. In East Germany, the economy was simply transformed into a socialist central planning economy which had price controls by design.