In the beginning, there was no need to fill in the legend, because there was no reason to suppose that Batman would become an enduring part of the landscape. Comic heroes came and went. Captain America, the Human Torch, the (Alan Scott) Green Lantern, the (Jay Garrick) Flash, the Black Terror... all those characters were gone from the scene after about 1949.
But when Batman did not join them in limbo, the writers and editors began filling in the legend for us. Obviously the first salvo in this effort was the expansion of Batman's origin tale in Batman #47. Over the next decade there were many stories that contributed to rounding out our understanding of the Caped Crusader, and for some reason, most of these tales were published in Detective Comics.
In Detective Comics #205, Robin asks Batman about how he initially found the Bat-Cave and:
And although elements of the story have changed significantly (for example, Bruce did not buy Wayne Manor but grew up it), the idea that he discovered the Bat-Cave by falling into it has endured, being depicted in Dark Knight Returns and in the Batman Begins movie.
The next bit of legend filling came in Detective #226's When Batman Was Robin. We learn how Batman first trained to become a detective:
As with several other stories in this era, this one contains some parts that contradict the legend. For example, Bruce explains that his parents were abroad that summer, but in the story he appears to be 15-16 or so, much older than most origins show him when Thomas and Martha Wayne were murdered.
Realizing that he needs to keep his identity secret, Bruce decides to wear a colorful costume (very much like Robin's down to the "R" monogram on his chest, so that Harris won't find out his real name. As Bruce learns detection, he must also be careful to avoid giving Harvey clues to his real name:
Of course, avoiding one clue means giving another; Harris learns from that exchange that Bruce's parents must be fairly wealthy. Over the course of the story, Harris teaches him many lessons, and in the end discovers his real identity. Harris explains in a letter (sent upon his death):
The concept of various experts training Bruce in the skills he would need as Batman was continued in Detective #227. Barret Kean is getting too old to play a leading role on stage or screen, so his agent suggests setting up a school to teach young actors about makeup. And fortunately, he has an old pupil who can vouch for his abilities:
And after an interesting case involving an attempt by the underworld to discover Batman's true features, there's a very similar ending to the prior issue:
Another one of Batman's experts is Lee Collins. Collins threw the boomerang as part of a sideshow act. He impressed Batman by helping him catch a crook, and:
So not only did Collins teach Batman how to throw, but he also created the very first Batarang!
I believe there is a story out there about the guy who taught Batman lock-picking as well, but I can't quite put my hands on it at the moment. It's possible that it's a more recent story. Anybody?
Another aspect of the legend was filled in with Detective #235. This issue includes the famous story, The First Batman. We learn that Thomas Wayne had worn a bat costume and fought crime himself, while Bruce was still a youngster. It happened that some crooks showed up at a masquerade ball which Thomas attended. This story also revealed that Bruce's parents were not killed by a happenstance robber, but that it was a planned revenge murder by one of the crooks Wayne pere had apprehended.
Detective #265 contains what appears to be the final story of the "Fill In the Legend" era, with Batman's First Case.
We see the troubles Batman had capturing his first crook, and the lessons that he learned from his experience. Incidentally, Bill Jourdain pointed out last summer, that particular story is a swipe from a Golden Age Robin story in Star Spangled. It was also the first issue published with the editor credit of Jack Schiff, which may (or may not) explain why it was effectively the end of the Fill In the Legend Era of Batman. By all accounts, Schiff was the de facto editor for years before that. And yet, from almost the moment he took over the Batman family officially, the stories changed dramatically.