1468 - M'gann M'orzz is hatched on Mars, the child of the White Martian terrorists that scorched the Martian surface. she is placed into stasis along with her tribe.
3 years ago - Human astronauts disturb the Martian stasis chamber, and M'gann's tribe go to Earth posing as alien heroes the Hyperclan. they attack the Justice League, decimating it's ranks, forcing Martian Manhunter to assemble a new League. When he finds M'gann, he takes her in to begin teaching her in both the Martian and Human tradition. She meets Emma, the daughter of J'onn's friend King Faraday and models much of her human behavior after her.
1 year ago - M'gann makes her first public appearance as Miss Martian when she, Natasha Irons & Traci Thirteen save Superman from Metallo. J'onn J'onzz introduces her to the Teen Titans. She goes with them into space to save Donna.
M'gann was first introduced as a new Teen Titans recruit during Infinite Crisis, not really being given a complete backstory. She started to be featured in the regular book soon afterward, her loyalty and motivation constantly suspect until the big reveal that she was in fact a White Martian.
DC has a poor record of keeping track of the status of the various Matian races. They are alternately all extinct or still thriving on the planet, depending on when the story calls for it. When M'gann debuted in Young Justice, they seemed to establish that the Mars was still populated.
None of this really mattered, because Miss Martian was absolutely incredible. She was such a fantastic character that she quickly became the face of the series.
We've had to skew somewhere between the series and the comic in order to fit her into the larger timeline. Martian society is long since extinct, due to a terrorist act by a clan of White Martians... the same White Martians that hid themselves in a stasis vault after the surface of their planet was scorched. M'gann was an infant, and when the White Martians are awakened on Mars and attack earth and the Justice League, J'onn finds the infant M'gann. This is the child of the terrorists that destroyed his planet, committed genocide on his people, and very likely killed his family. And yet, in an act of profound forgiveness and compassion, J'onn takes M'gann in. That moment perfectly sets the tone for this character that we all absolutely love.
This of course means that M'gann is much younger than she appears. In the TV series, she is described as being 48 years old, but maturing is obviously a very different process for a telepath. making her so much younger also gives her quite a bit in common with Superboy, although in the comics Superboy and Wonder Girl are one of the great romances in all of comics so unfortunately M'gann and Connor will have to simply be best friends, although I think there's something quite adorable about that. Also, we used M'gann instead of the Cir-el Supergirl in her team up with Natasha Irons and Traci Thirteen to stop Metallo, as it functions as a fantastic introductory moment for all three young heroes.