To win the war on the Eastern Front the Germans should have eased their racist anti-Slav policies. If they had backed the national committees that were established by different ethnic groups (Russian National Committee, Ukrainian, Belarusian, Georgian, etc.) then they could have had a potential source of millions of Soviets fighting on their side. The total number of collaborators with Nazi Germany from the Soviet Union is estimated to be more than one million at the very least, with the highest estimate being around 2.5 million.
Because of Nazi racial policies, the Hiwis (short for Hilfswilliger, German for "willing to help") and other volunteers, like Andrey Vlasov's Russian Liberation Army, were hindered and were rarely used in combat (the Battle of Stalingrad was one exception, where as much as one quarter of the German 6th Army's strength was estimated to be Soviet citizens). Although a lot of German commanders praised Soviet volunteers for being reliable and good fighters, they were ignored by the Nazis. General Field Marshal Fedor von Bock requested to Hitler that they put together a Russian Liberation Army of, initially, 200,000 men. However, the head of the OKW General Field Marshal Wilhelm Keitel told him to stay out of politics and did not forward his request to Hitler.
On the few occasions that Soviet citizens were used in combat they proved to be very effective. The ROA (the Russian acronym for Russian Liberation Army) fought against the Red Army in early 1945. They fought well and were praised by Heinrich Himmler and Joseph Goebbels for their vigor and ferocity. The ROA was better known for later defeating the Germans, ironically, at the Prague uprising. They managed to defeat the Heer and Waffen-SS divisions and drove them out of the city, saving the Czech partisans, who were on the verge of defeat before ROA's intervention.
The point is that they could have most likely toppled Stalin's regime if they had a policy of treating the natives better and actually used the Soviet volunteers in combat more often and effectively (many of them were sent to the Western Front instead). If they had, then the majority of the Red Army would most likely refuse to fight and defect in mass numbers. Even when the Germans were losing the war, they were still getting Red Army defectors. But this would have been probably impossible or highly unlikely at the very least due to the Nazi policies.
The only way I could see this possibly occuring is if high ranking Germans like von Bock and other generals, or perhaps Himmler (who backed the ROA and convinced Hitler to form ten Russian divisions in 1944, but it was far too late by then) went behind Hitler's back and allowed the formation and training of groups like the ROA and the national committees earlier on in the war; and also gave orders for better treatment of Soviet citizens. But that would have been highly unlikely to happen.
Lordganon wrote: 1 - Was never going to be nice to them. Have a look at "Mein Kampf" and you'll see why.
2 - That would mean the Brits let Germany dominate the continent. Fat chance of them letting that happen.
3 - Hello Soviet Invasion of Germany by 1943.
1—He could have been, as he decided to by giving the collaborationist groups fat more authority in 1945, but it was way too late by that point. And yes, I have read Mein Kampf.
2—The Germans could have let Brits have some territories.
Some possible theories:
1. During Operation Barbarossa, Hitler could have diverted forces from Army Group South to Army Group Centre and attacked Moscow with more force, so that the Soviet reinforcements from Siberia would be unable to change the tide. Taking Mosclw would have greatly benefited him. Also, he could have listened to Andrei Vlasov and Alfred Rosenberg to treat Slavs much better, and promise them an independent state after the war (even if not seriously). Millions in the USSR were willing to collaborate and aid the Axis, but they were not given any significant roles in fighting until it was too late, and the Nazis' brutality caused many to stop collaborating. These factors could have very well resulted in a Nazi victory on the Eastern Front, which was the most difficult one for them.
2. Strengthening relations with Britain before the war in order to form an alliance and remove them as an enemy. Hitler said he wanted to keep the British Empire intact and viewed them as a possible ally against the USSR. And some British Royal Family members had Nazi connections. Britain and Germany allied could have also at least tried to bully France to comply with them, creating a sort of pact between Germany, Italy, Britain, and France. These four countries would have virtually been unstoppable, at least to some extent.
3. Instead of breaking the Molotov—Ribbentrop pact, Germany could have allied the USSR and used that time to invade the rest of Europe, and not make any obvious preparations for an invasion until all other enemies were taken care of. After that, the USSR would have not had as many allies aiding it in various ways as happened in OTL (the US and UK opening different fronts and providing supplies, Greek resistance stalling the German invasion of the USSR, etc.)
Those are just some of my ideas.