An unidentified flying object could be anything from a bird to a plastic bag to a bona-fide alien spacecraft. Until we can tell what that weird thing up in the sky is, habit dictates that we excitedly call it a "UFO."
Let's not kid ourselves - usually we're pretty good at labeling what we're seeing, so if we can't tell, we assume that the strange glint up there isn't a T.V. satellite, but a pod full of little green men. What should you do if your eyes lead you to wonder? The seven most important things to keep in mind follow.
1) During the event, keep communication to a minimum. Don't talk to anyone around you. Whether you're seeing one or many lights in the sky, with our without a geometric arrangement, or something metallic moving erratically in daylight, don't say anything about it to anyone around you. Feel free to point and wave to get other people's attention, or call out a "look at that," but don't describe what you see aloud.
Don't listen to anyone, either. This point couples with the first. If the people around you are describing or discussing what they see, try to tune them out. Their words alone could affect whether or not you perceive windows in a craft, or how many lights you can count. You want to try to keep your memory as accurate as possible.
It is unnerving but true that no matter how educated, sober, intelligent and honest the members of a group are, each person is capable of constructing false memories about not only UFO sightings, but any supernatural, super-weird, or unexpected event they witness simultaneously. This is why, after robberies, witnesses are encouraged not to communicate with one another: it is likely to foil the accuracy of individual accounts.
2) Stay calm, especially if in a group. If you can't make yourself feel calm (which is likely, if you believe you're witnessing an extremely rare or special event), at least act calm, and give your brain reign before your feelings. Remember that "UFO" stands for "Unidentified Flying Object," not "alien spacecraft." All you know, as you look at the weird stuff in the sky, is that you can't be sure what it is. Don't allow that fact alone to convince you you're seeing aliens. After all, meteors, helium balloons and experimental military aircraft do exist.
Excited groups of people, especially when excited about extraordinary events, can develop a mob mentality, convincing one another to panic or behave rashly. Louder members can convince quieter members to believe they have seen what they haven't, for fear of being left out. Group hallucinations are very possible; they happen all the time. It's hard not to be influenced by groups in this way, so if you're in a group that's getting agitated or loud, step off to the side for a better perceptual view.
3) Document, document, document! During the event, use your camcorder, camera, phone, or even an audio-recording device to act as a dependable witness to the events. Note, mentally or on paper, the time, date, and place of the sighting.
Immediately after the UFO has disappeared, talk to your recording device while alone, or find a pen and paper without looking at what you've already recorded. Try to relax, and write out everything you can remember, without rereading or proofreading at all, until you're completely spent. You can rewrite your original copy more legibly later, but never throw out the original copy, as memories can erode and even edit themselves without your conscious permission. Include sketches of what you saw, as well.
4) Don't interfere with possible evidence, like the scorched earth of a crater. If you're one of the amazingly lucky (and some say nonexistent) people to actually witness what appears to be a UFO crash-landing site, don't touch anything, and don't get too close. You don't know what kinds of metals or energy sources you're dealing with, as the object is still unidentified. To tamper with it would be risking your health, and maybe even your life. Take as many pictures, notes, and video recordings as you can from a safe distance, and don't discuss them with anyone else present.
5) Remain aware of your fallibility. Be wary of your own judgments, and try to avoid being absolutely sure of any of your perceptions. No one is immune to perceptual construction or spacial misjudgment - not even you. In the past, airline pilots have misjudged their distances from UFOs (which usually turn out to be meteors) by thousands of feet. Multiple eyewitnesses in different locations have seen completely different things when looking at the same UFOs. All you can do is your best, and your account will be most valuable if you know your own limitations.
6) Don't obsess. After your documentation is finished, you may feel compelled to compare notes with anyone else who witnessed the event you did, as well as with documented eyewitness cases of other UFO sightings. The list of UFO sightings is a long and arduous one to get through. Topping that with all the speculation you could read and all the experts you could follow, an obsession with the theme of what you witnessed - aliens and government conspiracies! - might lead you only toward ill mental health.
If you find yourself cowering at your basement computer, obsessively chatting with other enthusiasts, or worse, developing an agoraphobic fear of being abducted, tell someone. A good friend will take you for a walk in the park and offer you a distraction from this mystery which, while probably being solvable, you don't stand a chance of solving all by yourself.
If, on the other hand, the sighting has simply piqued your interest in the direction of developing a new hobby, by all means, go for it! Learning about the scientific approach to investigating UFOs can't hurt: it could only help you by giving you the power to make your own educated and respectable judgments about what you saw.
7) Report your findings to multiple sources: believers, skeptics, agnostics, and the media.
Ufologists are known to be pseudoscientific sometimes, easily fooled by pranksters. Michael Shermer, a popular skeptic, writer and speaker, had children build mini-UFOs out of items like foil pie plates and plastic tubes. He mounted them on string, and then had the kids take black-and-white photos while the objects dangled over a precipice. The pictures fooled several ufologists, as well as most of the random people who were shown the pictures on the street.
Not all Ufologists can be discredited, but neither can all skeptics. Send your information to any UFO investigator you can find, as well as the more intensely skeptical, scientifically-rigorous folk. Don't fear disappointment: it's best to know what you really saw, even if it was a weather balloon after all.
The media eats up UFO sightings as well, so throw a copy of that tape in a manila envelope and ship it off to your local news station. Blogs and social bookmarking websites are another way to get your videos, pictures, and notes seen. You might be contacted by interested enthusiasts or investigators if you get enough views, but don't fear the men in black: that division faded out of service ten years ago, after Will Smith broke their cover.