How did batman meet the joker?

Answer 1

The first encounter between the Joker and Batman, according to them both, was before the Joker had even become who we know him as. At the time, he was Red Hood (How he got to that point is a mystery only Joker knows. And everytime he tells the story, he always changes it. But, it always ends the same). In the encounter, Batman cornered Red Hood in the Ace Chemical Plant where he fell over the railing and fell into the chemicals that would change both of their lives forever, giving Joker his iconic white skin, green hair, and red lips.The first time Batman met Joker as the Joker was in Batman: The Man Who Laughs graphic novel where Joker went on a killing spree through Gotham for the first time. His first attack was a building that became full of mutilated bodies after Joker had gotten to it. He made his public appearance at a social event announcing his next target would be millionaire Henry Claridge, who he does get to.
It all ends when Joker claims his targets Judge Thomas Lake and Bruce Wayne himself. Bruce is poisoned but eventually recovers thanks to the help of his trusty butler Alfred. He figures out that Joker's big plan is to poison the water supply with his Joker "serum". Batman ends up bringing the Joker to justice, stopping the flow of the poisoned water, and putting Joker into Arkham for the first time.

(NOTE: These events took place BEFORE the August 2011 "New 52" reboot DC Comics had. Whether or not these events happened the same way in the current timeline are unknown. For now, this is the most recent version of the Joker's and Batman's first encounter. Changes are still yet to be seen.)

Answer 2

Batman and the Joker first met when the Joker broke into a chemical plant and had a confrontation with Batman while trying to rob the place. This encounter led to the Joker falling into a vat of chemicals, which transformed him into the iconic villain we know today.