After reading the chapter "Hemispheres Colliding," in Guns, Germs, and Steel by Jared Diamond, you should address the following issues:
Why was Europe successful in conquering the Americas?
Why didn't it turn out the opposite way, with the people of the Americas conquering Eurasia?
Why was the European civilization more advanced (technology, agriculture etc.) than the native American societies they encountered?
Where you surprised by any of the evidence provided by Diamond?
The reason why the Europeans conquered the natives of the Americas can be summed up in a passage from p. 360 of Guns, Germs, and Steel. At the bottom of that page, Diamond tells us that, when Europe and the Americas “collided,” the Europeans
enjoyed big advantages over Native American societies in food production, germs, technology (including weapons), political organization, and writing.
This answers the first two question. Europe was able to conquer America (rather than having the Americas conquer Europe) because the Europeans had all of these major advantages. The important question, then, is your third question. Why did the Europeans come to have these advantages?
The answer to why the Europeans had all these advantages is the main point that Diamond is trying to make in this entire book. In this book, Diamond argues that the Europeans had their advantages because of geographic luck. They did not have advantages due to them having a superior culture, superior racial characteristics, or any other such factor. Their advantages stemmed solely from their geographic luck.
So what kind of geographic luck did the Europeans have? First, they lived on a land mass that had a large number of species of plants and animals that could be domesticated. Second, their land mass had a long east-west axis while the America’s had a long north-south axis. Because there were places on the Eurasian land mass with many domesticable plants and animals, agriculture was able to start there before it could start in the Americas (where fewer plants and animals could be domesticated). Because Eurasia had a long east-west axis (and no major physical barriers), agriculture could diffuse from one part of Eurasia to another. In the Americas, the long north-south axis and the barriers such as deserts, jungles, and mountains, made it hard for agriculture to diffuse from place to place even if it did get started somewhere.
These advantages meant that Europeans started to have food production (agriculture) sooner than Americans. This is very important because having agriculture allows a society to have other aspects of civilization. Agriculture allows them to have more technology (including writing) because it allows them to live in large numbers in one place permanently. This means that people can specialize in things like the creation of technology. It allows them to have more elaborate political organizations because those organizations are needed to control the large populations. It causes them to have infectious diseases because these diseases come to humans from their domesticated animals. All of these things (technology, which includes weapons and writing, germs, and political organization) allowed the Europeans to be able to conquer America instead of the other way around.
In short, geographic luck let Europe have agriculture earlier than the Americas. This made Europe more technologically advanced and allowed it to conquer America.