The biggest art fraud in modern U.S. history was shockingly simple. Yet it went on for 15 years, duped some of the world's most sophisticated collectors, brought down a 165-year-old New York gallery, and brought in more than $80 million. It is also a cautionary tale for anyone thinking of dabbling in the art world.

"Art and jewelry are the last sort of bastions of unregulated business," retired special agent Meridith Savona of the FBI's Art Crimes Unit said in an interview with CNBC's "American Greed." "If you're a collector, if you're in this art world, it truly is buyer beware."

Glafira Rosales first appeared on the New York art scene in 1995, showing up at the venerable Knoedler Gallery with a painting that she claimed was the work of abstract expressionist Mark Rothko. And Rosales said there was more where that painting came from. Claiming to represent a mysterious Mexican collector known only as Mr. X, she said she was helping him unload a collection of previously unknown works by Rothko and fellow expressionists Robert Motherwell, Willem de Kooning, and Jackson Pollock, among others. If true, it would be a treasure trove of modern art.

"This art is some of the most valued art of the 20th century," said author Maria Konnikova, who wrote about the scam in her 2016 book "The Confidence Game." "People paid tens of millions of dollars for it, and we haven't had anything new in it for a while."

But in fact, the art Rosales was peddling was the work of Chinese immigrant Pei-Shen Qian, who had previously made his living hawking portraits on the streets of Manhattan. Qian would imitate the styles of the masters, then "age" his work using substances like tea or dirt from a vacuum cleaner. It worked like a charm, with one purported Rothko abstract selling for $8.3 million, and a fake Jackson Pollock painting selling for $17 million, before art experts began to realize something was amiss.

In 2013, Rosales pleaded guilty to fraud, money laundering and tax evasion, and was ordered to forfeit $81 million. To date, she is the only person convicted in the case. Rosales, who cooperated with authorities and was sentenced to the three months she had already served in jail, said she was coerced into the scam by an abusive boyfriend, Jose Carlos Bergantinos Diaz. He is currently in Spain, having managed to avoid extradition to the U.S. on a 12-count federal indictment alleging fraud, money laundering, conspiracy and false statements. Also indicted were his brother Jesus, who is also believed to be in Spain, and Qian, who fled to China.

The Knoedler Gallery and its director, Ann Freedman, who said they were duped along with everyone else, have not been charged with wrongdoing. But facing multiple customer lawsuits, the gallery closed in 2011 after 165 years in business.

"If you enter into buying a work of art because you think it's going to be a phenomenal investment, that's a warning sign," Art Fiduciary Advisors managing partner Doug Woodham told "American Greed." "Stop, stop, stop!"

He said the Rosales case is an example — albeit an extreme one — of the perils facing art collectors and investors at all levels of experience.

"When you're thinking about buying a work of art, I think the first thing you have to do is say, 'What's the price of this relative to my income or wealth position and how comfortable would I be if this work of art ended up not being worth nearly as much as I paid for it?'," he said.

"If this work of art is $10,000, if in five years it was worth $5,000 or zero, how are you going to feel?"

If you are still ready to take the plunge into the art world, Woodham offers some tips.

"For a lot of people who are buying art, it's a hobby, it's a passion sport, it's something that they haven't done before and so oftentimes, people let their guard down," Woodham said.

He said it is important to know whom you are buying from. Large, established art galleries may be your safest bet.

"If you buy something from that gallery and it turns out to be a fake, or you'd like to return it and get a store credit, will that gallery be in a financial position to be able to do that? The smaller the firm, oftentimes the harder it is for them to provide those sorts of buyer protections," he said. "The larger the gallery, the easier it is for them to do that."

Of course, there was no gallery more established than Knoedler, which went into business in 1846. That is why Woodham suggests adding language to any purchase agreement to protect your rights should the art turn out to be fake.

"Try to get the gallery to agree that when you purchase the work of art that they're not in possession of any information that would call into question the authenticity of the work," he said. "Fraud doesn't have a statute of limitations. So, it's so important, when you're spending serious money, that you can put into a purchase agreement just a simple statement: 'The gallery is not in possession of any information that would call into question the authenticity of this painting.'"

If the seller will not agree to the language, that could be a red flag.

Woodham cautioned against buying art from a sole proprietor, or from a friend.

"Separate your personal relationship with them from the commercial transaction you're entering into," he said.

Woodham suggests novice investors study hard before even considering a purchase, specializing in artists, genres or periods that interest them.

"Maybe you want to collect women artists from the 1900s because you might think that they've been underrepresented or underappreciated," he said. "You may be interested in just collecting cutting-edge contemporary art. Finding an area of focus is important, because then you're going to learn how the marketplace works for that group of artists or that class of artists, and the odds of you being taken advantage of are lower."

He also suggests getting involved in the auction market — not as a buyer just yet, but as an observer.

"Start going to the major auction houses and seeing the works that are for sale in the important preview period," he said. That is typically three or four days ahead of the auction, when the works to be sold are on display for the public.

"You can now watch online the auctions take place, and so you can see which objects have lots of interest, lots of bidding activity, and then afterwards you can see realized prices," he said.

Becoming familiar with the artist or period that interests you can help you spot the genuine article. But determining the true origins of a work of art is a complicated mix of science, and, well, art. And it is best left to the experts.

The most important aspect is known as "provenance" — the pedigree or chain of custody of the artwork in question.

"You want to try and trace all those steps to make sure that it actually was in the artist's studio and that you know there were legitimate owners throughout that chain of command," Woodham said.

Another factor is called "connoisseurship." Experts on a particular artist or group of artists study things like brush strokes and signatures to help determine if a piece is genuine.

"You're able to stand in front of the work of art knowing lots of other work by that artist and be able to sense whether it's real or not," Woodham said.

Other experts use scientific testing of paints, canvasses or other materials to determine if the work is legitimate.

Finally, Woodham said, beware of anything described as "newly discovered" works of a famous artist. He calls that "the pond that forgers play in." It is also how Glafira Rosales' Mr. X collection was portrayed.

"I think if you're offered something that's newly discovered, and there isn't an exhibition history, and it's offered as a deal, run quickly," he said, "because that's, I think, a double flag that you've got a problem."

See how investigators and art experts finally exposed Glafira Rosales' massive art fraud, on the next ALL NEW episode of CNBC's "American Greed," Monday, Aug. 20 at 10pm ET/PT on CNBC.