In Their Own Words
I am hunting both for a copy of the Strand Magazines with Sir Arthur's fairy articles and for a copy of the British Journal of Photography with Geoffrey Crawley's examination of the photos. I do, however, have a copy of Sir Arthur Conan Doyle's book on the affair, The Coming of the Fairies (the copies of the five Cottingley photos in this article are from it), and I will slowly be adding the information from that text to this article. For now though, I would like to just give Sir Arthur's impressions of the photos, as is included with each within the book.

Picture 1, Frances and the Dancing Fairies

"This original negative is asserted by expert photographers to bear not the slightest trace of combination work, retouching, or anything whatever to mark it as other than a perfectly straight single-exposure photograph, taken in the open air under natural conditions."

As Geoffrey Crawley clearly showed in Arthur C. Clarkes World of Strange Powers, the negative that is presented in Sir Arthur's book has very obviously been touched up, though it is very unlikely Sir Arthur knew that.

Picture 2, Elsie and the Gnome

"The original negative has been tested, enlarged, and analysed in the same exhaustive manner as A. [picture 1]"

Picture 3, Frances and the Leaping Fairy
Picture 4, Fairy offering Posy of Hare-Bells to Elsie
Picture 5, Fairies and their Sun-Bath

"This negative [picture 3] and the two following have been as strictly examined as the earlier ones, and similiarly disclose no trace of being other than perfectly genuine photographs. Also they have proved to have been taken from the packet given them, each plate having been privately marked unknown to the girls."

Here Sir Arthur shows enough sense to protect against the possibility of being handed a different packet of film by the girls, but still doesn't consider the possibility of simple trick photography on the youngsters part. It proved a useless measure to mark the pack of film since the girls were then left alone to take the photos.

Variations
According to Jenny Randles in Strange & Unexplained Mysteries of the 20th Century, a "noted psychic" visited the small creek with Frances in August 1921, but though both claimed to see the fairies, no new pictures were produced. Randles gives December 1920 as the month the Strand Magazine ran Sir Arthur Conan Doyle's first article; I am attempting to dig up a copy. She states that Sir Arthur's belief in fairies was, at least in part, learned from his father, who had long reported seeing them; she also states that Sir Arthur's father had been diagnosed as mentally ill. She also gives Elsie's age as being 14 in 1917; and claims that Elsie insisted that the fifth and last photo was also a hoax, but Frances went to her death-bed insisting that it was the only one of the five that was genuine. She alsos say both women agreed on one other point; that, despite having faked the photos, they really had seen fairies and elves in the small Cottingley creek when they were young.
Harper's Encyclopedia of Mystical & Paranormal Experience describes Elsie and Frances as being sisters, which is clearly incorrect.

Theories
At the height of the controversy, many small problems were noticed in the pictures... ironically, these became arguments both for and against the authenticity of the photos. For instance, in the picture of Elsie with the gnome (the second picture), Elsie pointed out that you can see the head of the hat-pin poking out of the gnome's chest. Sir Arthur Conan Doyle saw it too... and explained it as evidence of a fairy navel, and took it as evidence that fairies reproduce in the same way as humans do.
In the picture of Frances with the leaping fairy (the third picture), it was pointed out that the fairy's farthest leg does not logically connect to the body, a problem easily explained when Elsie admitted she had drawn it wrong. But, at the time, the problem was hearalded as proof that they actually were pictures of fairies... the logic was that since fairies are etherial creatures, the misplaced leg was proof that the body was a temporary creation (this despite the importance Sir Arthur attached to the gnome's "belly-button").
It was noticed early on that the fairies looked oddly two-dimensional and in focus when compared with Elsie and Frances. It was also noted as strange that the fairies had very modern hairstyles. According to Jenny Randles in Strange & Unexplained Mysteries of the 20th Century, Elsie had worked for a photographer for some months; and according to the Times of London article from April 4, 1983, Elsie was earning money by coloring sepia photographs of soldiers fighting in the first World War that was still raging at the time. Hoax was also a suspicion because of the fact that the girls were only able to produce the photos when left alone. Unfortunately, this fact was defended by believers as an obvious necessity, since the fairies only trusted the girls.
Many believers argued that the fairies could be seen to be moving within the pictures; in 1984, Elsie Wright explained away this apparent proof: "...they said that ... they could see them, that the fairies were moving when the photographs were taken; but that's because they [the paper cutouts] did it [moved] in the breeze." [quoted from Arthur C. Clarke's World of Strange Powers.]
In his letter to the Times on April 9, 1983, Geoffrey Crawley states that the pictures were dismissed as fakes back in 1920 by the photographic technologists of Kodak... this announcement was followed by all access to the pictures being barred by Edward L. Gardner and, later, his son. In fact, according to Arthur C. Clarke's World of Strange Powers, Geoffrey Crawley suspects that the original photos were retouched by Gardner, who was a friend of Sir Arthur Conan Doyle, a believer in fairies, and the national secretary of the Theosophical Society; but in his letter to the Times on April 9, 1983, Crawley clearly points a finger instead at H. Snelling, a darkroom technician who made and sold prints of the photos.