The Joker's first actual appearance was in Detective Comics #168, although it wasn't as The Joker. It was as a man named Jack who would resort to crime because of needing money, which he did under the alias of Red Hood. However, during one of the robberies, he is cornered on a catwalk by Batman and chooses to jump into the chemicals below, knowing his breathing apparatus allowed him to breathe.
The chemicals in the vat would turn his skin white, his hair green and his lips red. Upon seeing this, he went insane and would become The Joker. Him falling doused with chemicals is the common source of him becoming The Joker, although the events leading up to that differ depending on the source. His true real name is never really known.
The Joker's first appearance as the criminal occurred in Batman #1, which came out in Spring of 1940. He was depicted as a violent sociopath until the late 1940s, where he would become a goofy trickster/thief. It wasn't until the 1960s that he would become a violent sociopath again. He uses a variety of deadly "toys," such as razor-sharp playing cards, as well as a toxic gas called Joker Venom, which makes victims laugh uncontrollably until they die.