How in the world did that work?
It didn't. This is the argument in image form, and you can find similar ones for employment (basically, when you conscript people, unemployment goes down. Shocking!). There are lots of libertarian articles on the subject--this might be an alright introduction--but the basic argument is that standards of living dropped (that's what happens when food is rationed and metal is used for tanks instead of cars or household appliances) but the government spending on bombs and soldiers made the GDP numbers go up, and then the post-war boost in standards of living was mostly due to deferred spending.
Note: as the article implies, the above viewpoint is not representative of mainstream economic consensus.
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