(1) Soviet forces overwhelmed the Wehrmacht by sheer numerical superiority: essentially, a four-year zerg rush.
(2) Hitler caused a great number of German setbacks by procrastination, recklessness, and stubbornness (e.g. a fixation on Stalingrad, the failure to cross the Neva in 1941, etc.)
(3) The Western Allies decided the outcome of the war when they invaded Normandy.
In Germany (3) is uncommon thanks to a general awareness that the Eastern Front consumed the vast majority of the war effort. (All my grandparents lost siblings in the Soviet Union; my grandfather fought as part of Army Group North from 1942 to 1945 and was a Russian POW until 1949.) (1) and (2), however, are widespread beliefs.
It's not difficult to see why. When German generals wrote their memoirs in the fifties, they were eager to exculpate themselves from responsibility for total defeat. Instead they blamed Hitler, who was unlikely to find vigorous defenders, and conveniently dead sycophants like Keitel. Of course Hitler was a bad commander-in-chief, terrible both at military judgment and at managing personal relationships with his generals; but in truth a number of people in the OKW would have found themselves with egg on their faces - like Franz Halder, who confidently noted that '[i]t's not too much to say that the campaign against Russia has been won within fourteen days' in July 1941. Collectively, the German generals easily displayed as much arrogance and short-sightedness as the Austrian corporal.
The Soviets, as pictured in German and Anglo-Saxon popular perception, were inferior to the Wehrmacht in everything but numbers. This sort of claim is at least partly a hangover from Nazi war propaganda: what was the Soviet Union but Asia's endless hordes threatening to overwhelm Western civilisation (the line adopted by the Nazis when they attempted to transform an opportunistic war of conquest into a pan-European crusade against 'Bolshevism' in 1942-43)? A few men, hopelessly outnumbered but superior in virtue, natural nobility, as well as technological and operational genius, fighting to the last against slavering barbarians - why, it's exactly the sort of romantic Thermopylae tripe the Nazis loved until the very end (see Kolberg).
In this racist fantasy the Soviets of course had to appear as the direct opposite of the noble Aryan: countless faceless goons (even though, as in the Battle of Kursk, numbers and losses were much more even than is commonly supposed), incapable of anything but mass charges (despite brilliantly executed operations like Operation Uranus and strategic offensives like Operation Bagration), indifferent to losses (there's some truth to this one, owing to the extraordinary situation of the Red Army in 1941-42, but from 1943 the Soviets were much more careful with their manpower), barbaric in their treatment of civilians (ignoring, like all empires, the systematic atrocities the 'civilised' troops committed against the populace).
It goes without saying that the Red Army was the decisive force in the war. Nazi Germany did not fall because it ran out of oil, and certainly not because of the Allied carpet bombing of German civilians: it perished because 80% of its armed forces were engaged and destroyed by the Red Army, and its conquered territories were occupied by the Soviets. In this the USSR was of course helped by supplies provided by the Western Allies; but it was Stavka that in extraordinarily difficult circumstances planned, and millions of Soviet soldiers that executed, the campaigns that brought European fascism to its knees.
In the First World War, Germany defeated the Russian Empire committing only a third of her forces. It's not to excuse Stalinism to note that Uncle Joe's assessment of the need to catch up in industrial development was spot on. By the 1940s the Soviet Union had become an industrial powerhouse. Soviet equipment was often of equal quality (the notorious German realisation, early in the war, that their tanks were inferior to the T-34 was not an isolated incident), but the Nazis' disastrous decision to focus on quality over quantity squandered what technological edge they did have, massively exacerbating the industrial disparity - another instance of Nazi racism digging its own grave.
Instead, having recovered from the initial shock, the Soviets relearnt the doctrine of deep battle their theorists had developed in the 1920s and 1930s. Deep battle, superficially similar to 'Blitzkrieg', is designed to break through to an enemy force's rear and occupy its territory. Unlike the Germans' unhealthy obsession with encircling and annihilating enemy forces (a fascination which, while going back to Clausewitz, was certainly favoured by Nazism's prejudices), the Soviet doctrine envisaged not physically destroying an enemy but confusing him, throwing him off-guard, and breaking his ability and will to act at an operational and strategic level.
Early attempts to put deep battle into practice were not unqualified successes, but from Stalingrad onwards the Soviets perfected the strategy, revolutionising the Red Army at every level. It was most impressively displayed in Operation Bagration, launched two weeks after D-Day. The offensive destroyed far more German forces than the Battle of Normandy, brought the Red Army to the borders of the Reich and, most importantly, shattered Army Group Centre and left the Wehrmacht in shambles. Before Bagration, German forces on the Eastern Front had been well-organised; afterwards, the Wehrmacht never achieved the same coherence and was soon forced to throw together Kampfgruppen, improvised formations of whatever was at hand in a sector.
In short, Soviet forces defeated the Wehrmacht because, from late 1942 onwards, they were the better army. Of course numerical superiority, present in most situations, helped, and so did the Soviet Union's greater industrial output. But all this would have counted for nothing had the Soviets not gained the skill necessary to disorganise and defeat the Wehrmacht at a strategic, operational and, yes, tactical level. The stereotype of an ignorant mass driven to the slaughter by callous commissars does a disservice to the bravery, motivation and skill of Soviet soldiers.