In the Golden Age, DC put out a couple oversized, omnibus books. Comic Cavalcade (initially) was dedicated to the All-American superheros: Flash, Green Lantern and Wonder Woman, while World's Finest (called World's Best for the first issue only) featured Superman, Batman, Boy Commandos and several other features. These comics cost a little more (15 cents instead of a dime), but they contained 92 pages, so it was worth the extra nickel.
Initially, there were no Batman and Superman teamups in World's Finest, with the notable exception of the covers, which generally featured Batman, Robin & Superman behaving like, well, teenagers. Here's a particularly amusing example:
But inside the book there would always be a Batman story and a Superman story, with no crossover.
That changed with World's Finest #71, July-August, 1954. DC decided to slim down the book to the standard 36 pages (including covers), and pare the price back to a dime. They maintained a couple of the backups (Green Arrow and Tomahawk), so to fit the other two features they were combined into one story.
This was not technically the first crossover of Batman and Superman. There was a one-shot teamup in Superman #76, in which (improbably) Bruce Wayne and Clark Kent share a room aboard a ship and accidentally discover each other's identity. However, outside the comics Superman and Batman had often paired up in the Superman radio series.
The first seven issues (WF #71-77) were illustrated by Curt Swan, who would go on to the great Superman artist of the 1960s and 1970s. But in WF #78 the series was (mostly) turned over to Dick Sprang. Sprang had been a longtime penciller of Batman stories and his style worked with Superman as well.
Sprang's specialty was perspective, and he always seemed to have the "camera" aimed in the right direction to give the reader the most entertainment. Here's a terrific example from WF #80:
Note that in the first shot, we get the crowd looking up at Batman and Robin, and in the second, we get almost exactly the opposite angle. This was a continuing theme with Sprang.
Sprang would go on to do the lion's share of the next 40 issues of World's Finest. Along the way there were a couple of significant stories.
In WF #88, Luthor and the Joker teamed up in Superman and Batman's Greatest Foes, a story in which the respective nemeses apparently go straight and set up a robot-building business together. Of course, it's just a front for a new criminal endeavor. This is the first super-villain team-up of the Silver Age and one of only a handful in DC history at that point.
World's Finest #90 featured The Super-Batwoman, the story where Batman decides to allow Batwoman to continue her crime-fighting career. He had forced her to retire in Detective #233 by discovering her secret identity, but now he was convinced that she had what it took to handle criminals.
In World's Finest #113, Bat-Mite and Mr Mxyzptlk teamed up. Although neither was truly a villain, this is still a significant early crossover. The Joker and Luthor got together again in WF #129, while Bat-Mite and Mr M renewed their acquaintance in #123.
By this time the editorial reins had been handed over to Jack Schiff and the stories suffered for a number of years with the same monsters, aliens and weird transformations that plagued Batman and Detective of the era. Dick Sprang only did three stories after WF #119, including WF #135's The Menace of the Future Man, his last work in the comics for many years. Schiff's own finale as editor was #140; in the next issue Weisinger took over this book, and that's a pretty good breakpoint.