If you look at the literature on the Great Depression, you will find that economists and economic historians cannot agree on why the recession began or ended. This may seem a bit odd, since it seems that history based on hard facts that can be measured in interest rates, GDP per capita, stock values, etc., would be more concrete than other areas of historical research, but it is simply not the case. Instead, it seems that the economy cannot be explained by mathematical models, no matter how much we wish that it could be. This is most clear in explanations of the causes of the Great Depression (an area of considerably greater research). The so-called monetarists such as Milton Friedman argue that policymakers could have avoided the Great Depression by increasing the money supply and mitigating deflation; the so-called Keynesians, such as John Maynard Keynes himself, argue that policymakers could have avoided the Great Depression by increasing government expenditures at the outset of the recession. Some economists argue that restrictions on trade aimed at protecting domestic industries at the start of the recession are what made the depression "great"; others argue that this had little effect. These are considered mainstream in economics today, but the list goes on.
Scholars do not agree on what ended the Great Depression either. Some say that the New Deal would have ended the Great Depression and that the Second World War only accelerated FDR's recover. Similarly, others argue that increased government expenditure at the outset of the war ended the depression (both ideas highlight government expenditure or "fiscal policy," in economics lingo). Others argue that fiscal policy did not directly improve the economy and that the recovery was "natural," i.e., that it was poised to happen anyway as a natural part of the business cycle and that fiscal policy, where it did play a role, was only a catalyst. In this view, the Second World War may have sped up the end of the Great Depression, but it was not an essential cause. Some economists, such as Christina Romer, argue that, just as a retraction in the money supply caused the Great Depression, an increase in the money supply in the United States that resulted from gold inflows (something which has evaded the popular memory, which focuses more on the direct actions of governments) ended the Great Depression. According to this interpretation, neither fiscal policy nor the Second World War played a decisive role in ending the Great Depression (at least in the United States).
In all seriousness, if someone else comes behind me and points to one cause of the end of the Great Depression, I will find you a paper written by a major economist published in a major journal that contradicts their claim. This is the nature of the field of history, of course, but in this case it seems especially striking to me because these papers are based on objective, numerical data. And while the consensus is that the outbreak of the Second World War ended the Great Depression, I think that the most honest approach for a historian would be to admit that the "truth" is unknowable and that we will all implant our modern political philosophies into our interpretations. The politics surrounding the Great Depression are, ironically I think, much easier to understand, because they were created by people with perceptions and ideologies that they could articulate. The economy articulates no such theories or agendas.
Using the standard definition of Depression, which is a reduction of GDP of 10% and a recession lasting two years or longer, the "bottom" of the recession in the United States occurred in 1933. That's when the losses stopped and the gains began again. However, much like the fiasco that you might be familiar with in 2008, the after effects persist significantly longer than the contraction.
By 1936 all economic indicators had recovered with the exception of unemployment, which remained abnormally high until the onset of the War. Rearmament and the war only fixed one problem, the stubbornly high unemployment rate. Going into the Second World War the unemployment stayed stubbornly above the 10% mark, after the war it settled into a more normal 5% range that we consider "natural" unemployment. So, in a sense, since the draft ended the last of the lingering aftereffects of the Great Depression, but unemployment is among the lagging indicators. It follows months or years after other conditions have changed.
There were several major contributing factors. A major drought and a collapse in commodity prices gutted the agricultural sectors of the economy while a series of retaliatory tariffs touched off in 1930 collapsed international trade and caused the industrial sector to suffer even more than it had been in the deflationary conditions caused by Gold Standard in a series of bank runs and loss of wages. Why would the Gold Standard lead to deflation? Well, the government needed to keep a certain amount of gold in the vault to cover people who wanted to convert dollars into gold. France decided that it wanted to increase its supply of money but it also was on a gold standard, so it increased the rates for gold. People in the US traded in USD for Gold for French Francs and converted Francs into USD at a profit, which reduced the amount of dollars the US government could put out which meant less money over all and therefore deflation.
Most of the initial reactions of governments in the initial running were simply bad ideas. The push to austerity and a balance budget in the beginning sharpened the decline by removing the government as a buyer of goods and an employer. The doubling down on keeping rates stable instead of letting market rates float contributed greatly to volatility in currency value which itself might have been a major cause of the depression. The "protectionism" that ended up cutting off overseas markets when they were most needed has never been a good idea, despite what labor unions might say. Then there was the belief among the Roosevelt Administration that the depression was a result of "too much competition" which led to the empowerment of labor unions and a series of bruising strikes until 1938, but more importantly led to the collusion of business leaders which kept prices higher than what the market would normally allow and making the average consumer functionally poorer and production levels abnormally lower.
That said, a number of the public works initiatives and the creation of things like the FDIC, Social Security, and the creation of trade schools and job training programs were unambiguous wins for the economy.
On the balance the government response likely triggered a temporary collapse in 1937 which lasted two years. The economy would have recovered a lot quicker with some different responses at the beginning, but the "recovery" definitively happened in 1936. The World War, especially the common use of "cost plus" contracts (where the profit of a company making war materials was a % of the cost of production which led to companies increasing wages and offering extensive benefits to increase profit) ended the era of the Great Depression in a way that no trace remained.
In short, to a random person on the street, they might still be unemployed in 1936 despite the fact that the depression was over for everyone else. Five years later almost no one was unemployed. That's pretty much the difference there. It was more of a perception that things were different and an improvement of the job market than the war actually ending the depression.