The seminal case in the whole constellation (sorry) of grey alien iconography and ideas is the Betty and Barney Hill abduction. A lot of the motifs we now take for granted came out of that one case, so it's easy to overlook how strange it seemed at the time.
(That said, many elements in it were shared with one or another UFO encounter - they just seemed to converge with the Hills.)
The Hills were returning home to New Hampshire from a vacation in Canada when they saw some lights up ahead on the road. The lights followed the car for a while, Barney pulled over to look at them through binoculars, noticed something that looked like occupants inside, started driving again... and then noticed they were 35 miles farther down the road than when they'd started, and somehow had lost two hours of time.
The details, though, came out later, after the couple underwent hypnosis to try to figure out what they'd been through. They were hypnotized separately, but by the same therapist. And they story they both told was that they'd been taken aboard some sort of craft and examined by "...bald-headed alien beings, about five foot tall, with greyish skin, pear shaped heads and slanting cat-like eyes."
Betty also drew star charts she recalled seeing, which were later determined (I'm not sure exactly how) to be of stars around what we'd recognize as Zeta Reticuli - the Greys are also known as Reticulans because of Betty's charts.
The case was investigated by J. Allen Hynek (the same fellow who came up with the "Close Encounter" scale - the "CEIII" or "Close Encounter of the Third Kind" being some kind of interaction with creatures aboard a UFO), who included his findings in The UFO Experience: A Scientific Inquiry, and by Stanton Friedman, who got a few books out of it.
Another go-to source on the Hills is The Interrupted Journey by John G. Fuller.
The University of New Hampshire also maintains a Betty & Barney Hill archive.
The image of the greys didn't end with the Hills, of course. Through Hynek (and, in all likelihood, Friedman and Fuller), the Hills' memories of Greys inspired the look of the aliens in Close Encounters of the Third Kind, an immensely popular film in 1977 which affected the way aliens were perceived by the wider culture.
Then, Whitley Streiber's [Communion](http://en.wikipedia.org/wiki/Communion_(book)), published in 1987, really cemented the idea that aliens were these thin, pale-skinned, dark-eyed, nearly noseless creatures in the public mind.
There are a few different theories as to what the Hills may have been seeing (or recalled seeing, which is a slightly different thing), which gets deeper into "when did it start".
One observation is that the Greys look like fetuses - they display neoteny, the possession of juvenile features by adult creatures. (Fetuses were not part of the Hill abduction, but became really strangely important in later generations of abduction narratives.) This could be a mental shorthand for "evolutionarily advanced", maybe.
They also have exaggerated eyes and minimized noses and mouths... a perception that some psychedelic drugs can stimulate (human brains produce DMT, a chemical linked with the feeling of communicating with entities, and that Dr. Rick Strassman has tentatively linked to UFO abduction experiences and Near-Death Experiences).
Or the big-eyed-ness might have some psychological significance relating to vision, or being watched... or even the process of being interviewed under hypnosis.
Or maybe the Reticulans come from a world of dim light and low ultraviolet radiation, so their skin doesn't need pigmentation.
But this is getting off the history track and into the ufology track, which is probably not where we want to be.
hi! there's room for more info on this image, but fyi, you can get started on this in the FAQ