If you know a little bit about a person, with some basic Internet search skills it's usually possible to figure out what he's been up to since about the late 90s. For example, if someone claims to have graduated from University A in 2003, and you find a few stale old pages mentioning him on UniversityA.edu, you can be pretty sure he's telling the truth. On the other hand, if you instead find him all over the much less prestigious JuniorCollegeB.edu, he's probably lying.
But this only applies to Internet-era events. You have little chance of proving whether someone spent time as a sword-swallower in the Barnum and Bailey Circus in the 1960s. If the person is roughly old enough to have done what he says he did at the time he says he did it, you won't be able to prove him wrong without going to extraordinary and expensive lengths, and even then you might never know.
There are some remarkable examples of people getting away with outrageous lies about their basic life experiences for years and years. The famous pilot Jackie Cochran claimed to have been orphaned and grown up dirt poor. In reality, she was neither orphaned nor poor, and the relatives who lived with her later in life were not, as she claimed, her adoptive family, but her regular old biological family. It's not clear why she lied about this, but the story was good enough to fool her friend Chuck Yeager, who repeated it in his autobiography, along with an anecdote about her having hired a private eye to search out her birth family, then declining to read the resulting report.
Then there's German politician Karl-Theodor zu Guttenberg, who was caught with a plagiarized Ph.D. from 2006, and an American academic named Leslie Berlowitz who said she had a Ph.D. but didn't. You notice that the 2006 case was only one of plagiarism, because that's harder to detect than an outright lie. Berlowitz said she earned a Ph.D. in 1969. Good luck Googling that one. I wouldn't be surprised if one in three Ph.D.'s "earned" before 1990 are completely fictitious.
I predict that people who are old enough will start making more and more fanciful claims about their pre-Internet lives. The basic human drive to make ourselves look like heroes has been taken away by Google - at least, it has for people who were not adults before 1995. Those who were will use the mists of time to their advantage.
By the way, did I ever mention that when I was in high school back in the 80s, I took first place in the Midwest Regional Science Fair for a project in which I demonstrated a hypertext protocol on my high school's computer network? No? Well, that fair merged with a much larger fair years ago, and their records have apparently gone missing, so you'll just have to take my word for it. I joke. The truth is, my high school didn't have a computer network, just a couple of sad old Apple IIs we wheeled around on AV carts. Or maybe it did. You'll never know!