Besides being hopelessly overextended, the main German mistake was leaving the northern and southern flanks in the hands of the inferior Romanian and Hungarian armies respectively. Both armies lacked proper anti task equipment and were not trained in the offensive German doctrines. Therefore, they were severely delayed in securing the banks of the Volga river as originally planned.
The Soviets recognized this and waited for bad weather to eliminate German air superiority. Then on November 19, they conducted a massive armoured push into the German flanks. Lacking proper anti tank equipment, being deployed in an offensive formation, and having no natural defensive barriers in the steppe, the Romanians and Hungarians were forced to pull back to the defensive positions along the Don River. The Germans were surrounded.
It's possible the Germans could have performed a breakthrough and retreat back to the Don, but Hitler personally ordered that Stalingrad would be held and the army would be supplied from the air until the flanks could be reestablished. Obviously, this plan was not feasible and the Germans lost thousands of men to the Russian winter and supply shortages. On February 2, the German sixth army unconditionally surrendered. For the first time, the Russians had the upper hand in the war.