How did The Red Army conduct itself in Germany exactly?

Mass rapes, summary executions, torture, mutilation. Looting and pillaging. The officer corps largely turned a blind eye to it (or actively participated). Those who did speak out were often silenced, and official reports ignored or fudged. Soviet propaganda had been painting Germans as beasts and urging its soldiers on to gorge themselves in violence against the enemy for months, perhaps without thinking through the inevitable consequences. Revenge was a particularly ubiquitous theme throughout the propaganda posters:
 

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“Open fire on murderers of our wives and children!”

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“Revenge!”

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“Revenge for the people’s misery!”

 
Soldiers were encouraged from on high to personally commit acts of revenge for every crime they had witnessed (or heard about) from the Germans. Command wanted to instill hatred into the conscript army as a primary motivator. And it worked; the Red Army was practically frothing at the mouth by the time it entered East Prussia. It succeeded to the point where command had to start backpedaling and trying (with varying degrees of success) to rein in the troops, as the regular atrocities were starting to seriously impact discipline.
 
Some quotes from historians on how bad things were at the start.
•Max Hastings, Armageddon: The Battle for Germany:
[Five days after the capture of Nemmersdorf], hardly one civilian inhabitant survived. Women had been nailed to barn doors and farm carts, or been crushed by tanks after being raped. Their children had been killed. Forty French prisoners of war working on on local farms had been shot, likewise avowed German communists. The Red Army’s behavior reflected not casual brutality, but systematic sadism rivaling that of the Nazis.
•Richard Overy, Russia’s War:
“In the first villages they occupied in October 1944 the soldiers slaughtered the population, raping and torturing the women, old and young. Refugees were shelled and bombed and crushed beneath the tracks of advancing tanks.”
 

Things got worse from there.

Officially, rape was a capital crime if a soldier was caught at it. In practice, it was ignored. Men and women who tried to save their children or families from being gang-raped in front of them were killed or mutilated, and then the children were shot or, in the worst cases, left crucified against a wall or door when the troops moved on. When Stalin was informed of the behavior of the soldiers he shrugged, saying:

“Imagine a man who has fought over thousands of kilometres of his own devastated land, across the dead bodies of his comrades and dearest ones? What is so awful in his having fun with a woman, after such horrors? The Red Army is not ideal, nor can it be. The important thing is that it fights Germans.”

The Soviets had ample cause for revanchism. Over the past few years they had lost, at a low estimate, twenty million people. Twenty million. Those who had fought and lived had survived against a foe who would offer them no quarter, who were reported to have committed atrocities against mass numbers of civilians. And these reports were starting to be borne out as the first of the death camps were being liberated. It seemed to the Red Army that the propaganda was almost downplaying what the Nazis were. The Germans were, in their eyes, monsters – civilians and soldiers alike.

What’s more, they were monsters who did not seem to have had any need to invade Russia in the first place. Houses in the German heartlands were filled with foods and goods that the Communist peasant soldier had never seen even before the outbreak of war, let alone what they had been living on for the past few years. I read a fairly amusing anecdote a while back about a unit who stumbled across a cache of a mysteriously oily white substance. The commander guesses that it might be lubricant for farm machinery. After two days, a private works up the nerve to try eating some of it, praying silently that it’s not poison (or just poisoned). When he wakes up the next day, he goes to the commander and says “I think I’ve heard about this stuff – it’s called ‘margarine’.” Whereupon the whole unit feasts on pancakes. My point is that it would be one thing if the Germans were desperate and looking for “Russian riches”. But these people were, comparatively speaking, living in the lap of luxury before they began slaughtering everyone to the east of them. When the Red Army discovered the truth of this for themselves, it just added more fuel to the fires of envy and rage.

The German forces also inadvertently made it worse for the civilian population by leaving behind large untouched caches of hard liquor. The thought was that a drunk soldier is a soldier easily killed. Unfortunately, an angry drunk soldier is all the more likely to join in the gang rape of the wives and daughters of the men who had invaded and killed their own families.

The Russians were also constantly exhorted to be on the look out for partisans, irregular troops who might attack the supply lines once the front moved past them. Which made for a handy excuse when looking to kill whoever they wanted to. And it was an excuse they often fell back upon, especially after the first of the death camps were liberated and it became clear just what had been going on even in the German homeland.

I don’t want to downplay the fact that everything the Soviets did to Germany had already been done ten-fold by Germans in Russia. And the people “returning the favor” were not the same troops who had started the war. Those were, by and large, already dead. By the time the Red Army arrived in Germany, a sizable portion of it was made up of violent prisoners released as an emergency measure, or prisoners of war who had felt brutality at the hands of the Germans themselves, or foreigners “recruited” at gunpoint with no reason to reflect well upon their unit and with resentment against both sides. But, regardless of any excuses or mitigating circumstances, it was still a horrific sequence of events.