I can't say that I'm an expert on Marvel's iteration of World War II, but based on the Captain America film I think I can take a stab at this. Essentially, the war played out similar to the way it did in our real world history. However, as this is a fantasical world, both Allies and Axis had superhuman and supernatural resources at play. So the war ended up roughly the same way as we know it, but in addition to the familiar battles during the war, there were amazing battles that Captain America fought, and amazing battles that Red Skull fought.
WW2 comics were pretty popular back in the day, so there were many comics like the Howling Commandos that showed various Marvel characters fighting in the war. These WW2 books essentially mean that the historical time frame is rich with Marvel heroes, but for the sake of keeping the Marvel Earth's history familiar to us, they do not dramatically alter the course of the war. WW2 didn't end years earlier or any such thing. Later historical conflicts still occurred in manners that we're familiar with, although Marvel stories may tell them with superheroes inserted into crucial roles.
On top of this, Marvel utilizes a floating/sliding timeline which allows them to maintain a semblance of stability in their heroes. Rather than having characters grow old and die as real-world time passes, they simply continue fighting crime in the "present", and their history is retconned into being much shorter in-universe. So instead of The Thing having fought in WW2, it's rejected out of hand as being ludicrous. Others, like Captain America, have their history altered to allow them to still fulfill key roles in history or to keep important parts of their history intact. Now the Marvel history books record Captain America as having fought in WW2, then being frozen for decades and thawed out in the modern day. Here "modern day" being the real world present, but this has been the case since 1964, so Cap has had 50 years of "modern day" adventures.
(Admittedly, many of what we refer to as "Marvel" heroes and villains of this era were not at the time actually under the banner of Marvel Comics as we know it today, as Marvel wasn't named that or they weren't the current owners of said characters at the time)