The Joker, real name unknown, is a homicidal maniac and the archenemy of Batman. Although his full origin is unknown, the Joker is known to have been forced to swim through a vat of chemicals which turned his skin white, his hair green, and left his face permanently locked in a double Glasgow Grin. Completely unpredictable with no regard for human life, the Joker finds murder and mayhem funny, and is perhaps the most dangerous man on New Earth with a body count stretching into the thousands, all centered around his obsession with destroying the Dark Knight.
The Killing Joke
Accounts of the Joker's origin story have been varied and numerous. He himself has told the story of how he came to be in several different variations, saying that sometimes he remembers it one way, sometimes another; and that if he has to have a past, he "[prefers] it to be multiple choice." What has remained the most consistent is that his first encounter with the Batman was while he was acting in the identity of "The Red Hood" with a gang of other thugs, committing a robbery in or near the Ace Chemical Processing Plant. He either tripped into a vat of chemicals, or was accidentally pushed in by Batman.
Most origins end with him falling into chemicals which bleach his skin and make his hair green and gives him a permanent red smile. They also always end with him either being forced into criminal acts or committing them himself. They invariably include Batman's involvement in some way.
For whatever reason why he may have fell into the vat of chemicals, he blames Batman. The event is a catalyst to his insanity due to possibly the combination of exposure to the chemicals, possible brain damage due to oxygen deprivation, or his growing hate towards Batman. During a lucid state  the Joker admits "Here's the cold, hard truth Bats...I don't hate you 'cause I'm crazy...I'm crazy 'cause I hate you.
Batman's first fight against the Joker
His activity between then and his first public appearance as The Joker is unknown, but his return to the Gotham City crime scene was a spectacular one. He announced himself on television, after murdering a reporter with Joker Venom, and publically told the police he intended to murder local millionaire Henry Claridge that evening at the stroke of midnight. Despite a full compliment of GCPD officers guarding his apartment, and intervention by the Batman himself, sure enough at midnight Claridge collapsed to the ground in a fit of laughter and died with the Joker's trademark death-grin on his face. The Joker would nearly contaminate Gotham City's entire water supply with his poison, but Batman was able to stop him by cutting off the reservoir's connection himself; effectively forcing the entire city into a drought as a consequence. The Joker was successfully incarcerated, but not for long.