My understanding is that the German's main goal during Operation Barbarossa was the capture of Moscow. This never happened, but if it had did they have further plans after this? Surely they were aware of Napoleon's "welcoming" in Moscow.
They did had a plan, if you can call it that. The plan was, hit the USSR hard and watch its collapse. In retrospect this sounds mad, the USSR and Stalin proved to be much more stable then anybody thought. Hitler belived the same thing that happend in WW1 would happen again, he thought the USSR was not stable and would collapse, specially if the capture moscow.
I dont know that we know much of hitlers plans for the east beyond the ones he wrote down in his book. He wanted to remove that 'bad' races and expand the lifing space for racial germans to the east. How they would handle this administratively is not known (at least I have never heard or read anything about such a plan).
I think a good guess would be to look at there adminstration of countrys like poland for a model of what would have happend to ruissa at least in the short term.
After capturing Moscow I would assume that most of the German Resources would be shifted to capturing the Oil Rich areas of the Caucasus to fuel the German War Machine. As vertexoflife said the Remaining Forces would be used to crush any remaining Soviet Resistance