Germany's economic rebuilding came mostly between 1924 to 1929. The economic policies that made this happen was the following:
A return to the gold standard
Up to 1924 the German government would simply print more money to pay its debts and this led to hyperinflation. A return to the gold-standard stopped this.
A liberal business-friendly market economy made industry prosper, and a liberal tax-financed social security prevented the worst forms of poverty.
Since the German economy had collapsed, the Dawes Plan was put into place to save Germany and lessen the impact of the war reparations. As a part of this Germany would loan quite large amounts of money from American banks.
These three parts worked together to stop the German economic collapse and rebuild it during what has been called "The Golden Era".
Hitler continued the last policy of borrowing large amounts of money after 1933 as well and used it to finance the German re-armament.
What can current governments learn from this?
Having a gold standard has other drawbacks, but it's better than hyper-inflation. However, an even better policy is to not have a gold standard, but have a politically independent central bank whose job it is to keep inflation within reasonable limits. The Euro already has this, so nothing can be learnt from that.
A liberal capitalist welfare state is a good idea, and this is also indeed the most common type of economic policy in Europe, so this lesson has been learnt as well.
The current crisis simply has its basis in related but slightly different problems. Many states in Europe have paid their debts by borrowing money instead of printing more.
Borrowing large amounts of money to kick-start your economy is a common political policy and inter-war Germany is a good example of this, so this lesson has been learned. The lesson that has not been learned is that you need to pay it back.
When the depression hit the United States in 1929, the banks would retract the money from Germany, making Germany one of the worst hit countries in Europe (arguably paving the way for Hitler). Hitler never paid back his loans (it has even been argued that the massive loans he took was one major reason for him to start WWII as Germany couldn't actually pay them back).
The basic idea behind this Keynesian policy is to borrow when times are tough and pay it back during better times. However, many European countries have instead continued to borrow during prosperous times as well, to be able to implement popular policies as lower taxes or higher welfare. This is the fundamental root to the current European crisis. And that means that although they learned the lesson that you can't pay your costs by printing money, they did not learn the lesson that there's no such thing as a free lunch.