I know that he reached Moscow, but did Napoleon actually keep any sort of garrison there for any amount of time?
The Russians, when they had to defend against powerful advancing forces, like Napoleon's army, were forced to use the policy of "scorched ground". They would burn the crops and poison the wells so that the French couldn't resupply on the way. Since Russia was (and is) Huuge, you had to march a lot. Being low on resources would be very bad.
Anyway, Napoleon defeated the Russians before he reached Moscow. Knowing that Moscow would fall, the Russians burned Moscow, before Napoleon got there. They did not want their city to fall in the hands of the French.
By that time, Napoleon thought he'd won. He remained in Moscow for some time, but Russia wouldn't surrender. As winter came, many soldiers died because they were ill-prepared for the harsh Russian winter.
Napoleon realised that his army was starving and freezing, so he retreated to France. On the way, sneak attacks and attrition took a heavy toll on the French army.
In the end, Napoleon entered Russia with one of the most amazing armies in the world until that time, and returned with less than 10% of it.
Home, Austrians, Prussian and English were waiting for him. He lost and got exiled.