What can we, as a species, learn about the threat of hostile extraterrestrials from Columbus' discovery of the New World and the subsequent extermination and subjugation of its Native inhabitants? There were many factors behind the colonization of the New World, most of which are readily obvious. From those factors, we can understand what allowed European powers to overtake Native American societies, and how we can prevent hostile extraterrestrials (henceforth referred to as "HE") from doing the same to the human race.
The most apparent advantage which Europeans possessed over inhabitants of the New World was much more advanced technology. Europeans had gained gunpowder, powerful navies, propaganda, written records, and countless other inventions during the course of history. On the other side of the Atlantic, complex societies such as the Aztec and Inca empires lacked the wheel, and no way of crossing the Atlantic. Due to this technological gap, European monarchies easily and quickly crushed even the most advanced Native nations.
An equal, if not larger, technological gap would likely exist between the human race and any HEs (this, of course, assumes the HE contacts the Earth first, and not vice-versa), as interstellar transport would only be possible with thousands, if not millions of years of technological prowess over humanity. Along with spacecraft, the HEs will likely bring weaponry as of yet not conceived by the human race, medical abilities far beyond our own (to be discussed later), and other inventions we, much like the Native Americans, could not understand at the present date.
How, then, are we to respond to HE technology? In the same way many Native societies responded to European technology: adapting to it. Within several generations, the Comanche tribe of the Great Plains had become skilled on horseback, despite never having encountered them before the arrival of settlers. Many tribes learned to use gunpowder and muskets along with traditional bows and arrows. In one notable example, the Cherokee silversmith Sequoyah developed an entire syllabary for his people based on the Roman alphabet, despite being unable to read or write.
In the same way, the best hope for humanity would be to gain, either forcefully or through negotiation, HE technology. While early usage of weaponry would be restricted to simply using the weapon until it breaks down or is destroyed, efforts would be made to reverse engineer and recreate the item. In the case of the new technology being an abstract concept (e.g. a new system of writing, new way of government), simple observation and interrogation will help us understand the technology.
While technology was a major boon to the European conquest of the New World, the largest killer of Native Americans was European disease. Millions of New World inhabitants died of illnesses such as smallpox, measles, tuberculosis and cholera. At the same time, very few Europeans died of Native American diseases. This was a result of the crowded living conditions in Europe at the time, in which many people were living very close to each other, rarely bathing, and spreading disease. Over centuries, most living in the cities developed genetic immunity to the diseases. When the first colonists reached the New World, the Native Americans were simply unprepared for such powerful, quick diseases, and suffered as a result.
Diseases, in the context of pop culture, are often viewed as the quick, easy solution to an alien invasion. One notable example is H.G. Wells' The War of the Worlds, in which bacterial infections kill off the entire invading HE force. Though it makes an excellent deus ex machina, bacterial infections would likely be of little danger to HEs. As it was previously mentioned, Europeans lived in much more dense, crowded cities than Native Americans, and it is just as likely that HEs would live in much more dense, crowded cities than human beings. This, coupled with several thousand to millions of extra years of development would result in far more deadly diseases to which we would have no immunity. Even if the HEs exhibited a crippling weakness to human disease, the advanced medical technology in their possession would quickly solve the problem.
All hope, however, would not be lost in such a scenario. Just as many people today fail to receive vaccination against illnesses which are no longer common (foremost among them smallpox), it can be presumed that HEs would have failed to continue immunization efforts against diseases they considered eradicated. By recreating the disease, or at least introducing one very similar to it, a major outbreak could be triggered, much like a smallpox outbreak today. Sabotage of medical equipment and selective assassination of medical professionals would further progress of the disease.
On a final note, in the event of contact with HEs, our species will likely be viewed as "lesser", despite any attempts to prove otherwise. Evidence for such an idea is seen in the multitude of explanations given by religious and government officials to justify the extermination and enslavement of Native Americans, among them a lack of a soul, a need to be "civilized", and that the conquest was God's will. HEs will view humans on the whole in the same light, and treat our species as such. We must be prepared for this moral system, and use it to our advantage. In retaliation, we must remember that an overt attack by HEs would not be a war for hearts and minds, but for all out conquest. We must not make the same mistakes made by the Aztecs, Inca, and countless others.