If you are really interested in this you should read "Unravelling Piltdown" by John Evangelist Walsh. Fascinating stuff but a bit dry in places.
According to Walsh, and I have no doubt he is correct, the hoax was put on by Charles Dawson, a country lawyer who practiced south and east of London. Dawson was a fossil hunter from way back and was friendly with a fish expert, Arthur Woodward, at a natural history museum in London. Early in 1911 Dawson appeared at the museum with some pieces of a cranium that he said had been taken from a gravel pit near Piltdown Common. He was never quite clear about how or when he had first got them.
Subsequent digs at the pit by Woodward, Dawson and Tielhard de Chardin over the next two years found more things that could have been associated including more cranium fragments and finally about half of a lower jaw. The cranium was very thick but looked human, the jaw was undoubtedly like that of an ape.
But the part of the jaw that joined the cranium was absent, and even then it was known that the human jaw has a differently shaped joint to that of an ape, since the human jaw can move from side to side while the ape one can hardly do this. A couple of teeth in the jaw looked human as they had a pattern of wear that looked as it they had moved from side to side. So it could have been once attached to the cranium.
This indicated that the human cranium had developed before the jaw, whereas the most prevalent theory at the time suggested it was the other way about, or that they developed together.
When some doubts were expressed, Dawson then reported the finding of a tooth at another site nearby which was consistent with the ones in the jaw. He never said exactly where this was and in fact died suddenly soon after. The new tooth was taken as confirmation. The tooth eventually was given to Woodward at the museum.
Not all scientists accepted the association of the jaw and cranium. In the USA, the leading expert at the Smithsonian said it was a mistake and the main French authority, Boule, said so too. Even in England, Arthur Keith, an expert at the anatomy museum thought it was wrong at first, but when a revised reconstruction of the skull was produced he accepted it.
By the 1920s the Piltdown skull was regarded as an anomaly in England and by the 1940s it was almost disregarded. After Woodward retired from the natural history museum he spent the rest of his active life looking for more Piltdown material and never found anything.
As has already been said, new age testing methods showed the fragments were more modern than first thought. That did not dismiss them entirely, but in about 1953 more tests showed they were fake.
The man who first detected the fakes went straight to Hastings where Dawson had lived and asked around. Some of the local people who had known Dawson 50 years before and were still alive had been convinced all along that the thing was a fraud! Why? Dawson was locally known for producing things of doubtful authenticity and one woman showed him a cabinet of fossils that her late husband had said that Dawson had faked.
Tielhard de Chardin, a Jesuit priest and first world war hero was well versed in anatomy and anthropology. After the fraud was exposed, he claimed he had been suspicious of Dawson for years. While that might not have been true, he never referred in writing to his personal involvment in the Piltdown case after about 1923.
What the lesson for science has been is never to take anyone's word for anything. Any finding must be backed up with time, date and place. That is even more so when the find is controversial. People should have been suspicious when Dawson never said clearly when and how he got the original cranium fragments, or where the confimatory tooth had come from. But they were not suspicious. Woodward had known Dawson for nearly 30 years and trusted him, so I suppose it is excusable.
EDIT Another lesson which has not yet sunk in is that just because someone does not have formal qualifications, it does not mean they cannot have expert knowledge of some field. Dawson, a lawyer, had no formal qualifations in comparative anatomy, but he clearly knew his stuff about the joint of jaw to cranium, and broke the awkward piece off before he planted it.
Second edit - 1911 in the second paragraph should read '1912'.