The short answer is they didn't. They suffered from massive debt before, during, and after the war.

Fascist economies are wildly inefficient and rife with corruption and the Great Depression continued to slow trade globally and in Germany before the war. (Imagine a government run by the mob where everyone takes a piece of every sale and it concentrates in the hands of governing authorities who either ignore laws or abuse them for their own benefit) The government further bankrupted itself by spending massive amounts on military arms and social welfar programs they couldn't afford.

They "paid" for the war through confiscatory policies, printing money, faulting on loans owed to foreign countries they were at war with, slave labor, and mass pillaging on and individual and governmental scale. Individual businessmen bought into and accepted the system because they were issued massive payouts on war contracts and benefited from preferential treatment (Receiving the homes and property recently stolen from Jews fleeing Germany in the 1930s or murdered during the war)

They paid soldiers by permitting them to purchase luxury goods in foreign countries at extremely discounted prices. (The German mark was valued in a foreign country at a rate higher rate by the barrel of a gun) They then sent these home to their families who would sell them on the black and or open market. This tended to help when the checks didn't show up on time.

A good book on this is Gotz Aly's "Hitler's Willing Beneficiaries." It is very good.

It is worth mentioning that they also took a lot of money from the seizure of Jewish, Polish, and other undersierables asset's. These assets include some vast fortunes, lands, and factories. This helped to supplement the costs that the Germans inured while they were on the March. They also used these people as forced labor. POWs and prisoners of all types were used for labor, there were over 600 individual slave labor sites at the peak of the war. They were used in many manufacturing steps of the construction of war material which went a long way to free up native German workforce, and drastically driving down costs.

The Germans also started to cannibalize the infrastructure of conquered nations to meet the needs of destroyed infrastructure elsewhere. Many Russian, French, and Polish factories where stripped of their machine tools. the Germans had a special machine that they used on the back of their trains that would allow them to rip up long sections of rail at a time and send the iron back to Germany to either be reused or recycled into more war material. The Germans where very efficient when it came to harnessing the full value of the nations that they conquered, and if there was opportunity there was very little hesitation to send valuables found there back the the industrial heartland.

Adam Tooze wrote a huge book on the subject that I was only able to get halfway trough, if you are interested it is really worth the time, but can be a slow read. The Wages of Destruction: The Making and Breaking of the Nazi Economy

Picture of Germans ripping rails, The rail attachment that does it.

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