A few things to learn from Aliens ;)

If you've ever seen the 1951 sci-fi classic The Day The Earth Stood Still, you may remember the scene in which the flying saucer lands in Washington, and Klaatu the alien emerges, holding in his hand what looks to the terrified humans like a weapon. After a soldier shoots Klaatu, Gort the robot emerges from the spaceship, and employs his otherworldly powers to disarm the soldiers and reduce a tank to scrap metal. It's only then that the wounded Klaatu rises to reveal that what he had in his hand was a miniature telescope, capable of seeing father into space than existing human observatories. From the script:

KLAATU: It was a gift. For your president. (Glances at the broken object ruefully) With this, he could have studied life on other planets.

Okay, that was just from a movie. But the paradox that the scene raises might well turn out to be a real one, if we ever actually make contact with terrestrials, who most likely will come from a vastly more advanced civilization. While we're likely to fear aliens, assuming that they're out to conquer and/or destroy us, it well be that they're actually benevolent creatures who want to share with us what they know. And what they know might have the potential to help us an enormous deal.
In a 1995 report, the U.S. Naval Observatory's Steven J. Dick wrote that discovery of an extraterrestrial civilization also would have potentially mind-blowing impact upon science and our view of reality, comparable to Europe's rediscovery (through the Arab world) of classical Greek science in the 12th and 13th centuries, orCopernicus' discovery in the early 1500s that the Sun, not the Earth, is the center of our solar system.
Here are a few areas in which I think we could make enormous progress as a result of contact with an extraterrestrial civilization:

• Unlocking the secret of faster-than-light travel. Presumably, aliens who visited our planet would come from an enormous distance across interstellar space, since even the nearest potentially habitable planet is probably at least 13 light years away. That might mean that they have developed a technology similar to the warp drive envisioned by theoretical physicist Miguel Alcubierre, or something else that is at this point beyond the human imagination. They may also possess antigravity technology as well, since UFOs (assuming that at least some of them actually are alien spacecraft) have been observed to perform seemingly impossible aerobatic feats. 
• Freedom from the limitations of our biology. Humans already are beginning to dabble in transhumanism--that is, augmenting ourselves with powered exoskeletons and electronic gadgetry such as microchip implants that enhance vision. But if an intelligent extraterrestrial species has been around for longer than us, it may well be that they've become completely post-biological creatures whose brains merge natural and artificial intelligence. They may even have discarded their meat bodies completely to live within machines of their own creation (which hopefully don't look like circa 1991 Arnold Schwarzenegger--that would be too weird). Here's a 2006 paper by NASA scientist Steven Dick on that subject. We could make a quantum leap forward toward transhumanism with their help.
• Reversing environmental damage. It's conceivable that extraterrestrials from a far more advanced civilization have mastered planetary engineering--that is, the ability to make major intentional alterations in the environment. (Here's a paper that Carl Sagan co-authored on that subject years ago.)  That might enable them to fix our atmosphere and reverse the destructive process of climate change. 
•  Conflict resolution. International conflicts are killing people at a far lower rate than in the past--about 55,000 people are dying worldwide from warfare each year in the 2010s, according to Foreign Policy magazine, about a third of the fatal casualty rate in the 1980s. But humans still possess an alarming propensity for slaughtering one another, as evidence by the estimated 468,000 homicides committed worldwide in 2011, according to United Nations research. If an intelligent extraterrestrial species has been around for longer than us, most likely they've developed lethal technology at least as potent as ours, and possibly even more so--imagine something along the lines of the Death Star from the Star Wars fictional universe. But the aliens' continued existence would mean that they also have some advanced method for resolving differences without violence. We might be able to get them to share that method with us--or perhaps, as a last resort, to send a legion of Klaatus and Gorts to force us to stop the killing.