How did the division of Germany lead to the Cold War??
I guess you could say that the division of Germany led to the Cold War, though I would say it was more a part of the Cold War than its cause.
You could say it led to the Cold War because it gave the USSR and the US something to fight/argue over (instead of being separated and never really coming into contact).
Because of the division of Germany and of Berlin, the Berlin blockade happened, with the Berlin Airlift coming soon after. Because of this, the Berlin Crisis happened in 1958.
So overall, you could say that the division made a lot of things for the USSR and the US to argue and get mad at each other about.
One thing, though -- my guess is that there is something specific in your book or your lecture notes that your teacher will want you to talk about. You should probably look for it.
The Cold War was a function of the United States and Soviet Union, with their conflicting ideologies, coming into contact with each other all over the world. The era can be defined as from about 1945 to 1989. Germany divided simply because the Soviet Union invaded from the East, and the other Allied countries invaded from the West during the conclusion of the Second World War. Ironically, the Allied forces could have continued eastward, but were halted; the meeting of both armies at the Elbe River in April 1945 split Germany, was the end of the Nazi regime, and was the beginning of a half century of posturing and international intrigues between the two "superpowers."