When Medivh opened the Dark Portal and the orcs began to venture into Azeroth, Garona went with the scouting parties. On one of these adventures, her party attacked Medivh for ... some reason. Damn ungrateful orcs! Medivh killed off the war party, but left Garona alive to give a message to Gul'dan. When she returned to Gul'dan, he decided to send her to stay with Medivh permanently as a spy for the warlocks. She arrived at Karazhan as the "Emissary from the Horde", although Medivh knew exactly what she was up to, since he's the world's most powerful mage and all. But since she was a rogue, he figured they needed her for Shade of Aran and would rotate her out for a warlock afterwards. (Zing!)
Medivh's apprentice, Khadgar, didn't know that Medivh had been the one to bring the orcs into Azeroth and was upset at Medivh for receiving Garona as a Horde emissary. Nevertheless, Medivh commanded the human and the half-orc to get along, and eventually the two turned from mortal enemies to friendly rivals. Garona told Khadgar that the orcs had come to Azeroth through the Dark Portal. Garona also began to respect Medivh's accomplishments as a wizard, and felt that she couldn't betray his trust by actually reporting his activities to Gul'dan.
And that's why when Medivh started acting strangely, Garona decided to work with Khadgar instead of going back to Draenor. Together, Garona and Khadgar discovered that Medivh was the guy who opened the Dark Portal, and saw his plans to use the orcs to destroy the humans. Garona was not too happy about her people being manipulated by Medivh, and she and Khadgar tried to fight their master. They would have been doomed, but Khadgar created a vision of Medivh's mom to distract him, and the duo ran from Karazhan to try to find help.
Khadgar and Garona went to Stormwind to see Lord Anduin Lothar and King Llane Wrynn about Medivh. During this time, Garona became a good friend of Llane. They eventually convinced the humans of Medivh's treachery, and the heroes headed back to Karazhan to put down the mad wizard. While roaming Karazhan, Garona came upon a magic mirror that showed her a vision of her future self killing Llane. Garona was horrified, but Khadgar helped her snap out of it and reminded her that they were here to fight Medivh, not play dress-up princess in the mirror. (Actually, he said that if the vision was true, then at least they'd make it out of Karazhan alive. Way to comfort.) Finally, Garona, Khadgar and Lothar confronted Medivh. An angry Garona launched herself at Medivh, but he struck her down with a magic spell that clouded her mind, telling the party that he thought that she would understand him since she was a spy. While she was incapacitated, Khadgar killed Medivh, sending Gul'dan into a coma. But after the battle, Khadgar and Lothar couldn't find the half-orc.
Medivh's spell had confused Garona. She was unsure of where her loyalties fell. So when the Shadow Council sent her orders to kill Llane, she slipped away and headed to Stormwind. She was caught by Lothar, however, and imprisoned as a spy in Northshire Abbey. She was freed by the orcish Horde and returned to Stormwind. Despite not really wanting to do it, she killed her friend Llane Wrynn and cut out his heart to return to the Shadow Council. Awesome! However, instead of offering her a cool drink of water and a hot bath, the orcs (now under the leadership of the anti-warlock Orgrim Doomhammer) tortured her until she told them where the Shadow Council was holed up. This whole timeline is incredibly messed up, because Lothar sent Garona as a prisoner to Northshire Abbey either for being a spy (before Llane's death) or killing Llane (after it) and she was freed by either Shadow Council or non-Shadow Council orcs. Also, Garona may have given Llane information on the Horde either before or after Medivh's death. Blizzard needs to get their story straight. Anyway, Garona survived the torture, gave up the Shadow Council to Doomhammer's orcs, and slipped away again.
Where she is now: No one knows. Officially, Garona has not been seen since the First War, although Blizzard repeatedly hints she's going to be in WoW in some shape or form. In WoW's closed beta, Garona was indeed in-game as the grandmaster of Ravenholdt Manor (the rogue faction), but she was removed before the game went live. Currently, she's "in-game" in two places -- the rogue Dire Maul book is named after her, and you can find her Signet Ring in Karazhan loot tables. However, she is a rogue, and therefore could really be anywhere as long as she's hiding.
Identifying features: She looks like a thinner, prettier female orc. She has red and orange tattoos on her green face and upper body, and has a skull motif going in her necklace and braids. She wears the red Breastplate of Bloodthirst.
Who's her daddy: So Garona's definitely a half-orc, but the other half of her parentage is unknown. Originally, she was a half-orc, half-human, because the first version of the First War had fifteen years pass between the first orc parties into Azeroth and Llane's death. Garona could have been a teenager when she killed Llane. But later, the First War was "retconned" into only lasting one year, making that unlikely (although orcs apparently have a spell to age their children up to fighting age.) Blizzard community manager Caydiem said Garona was half-orc and half-draenei, but Garona's remarked about humanoid parentage before and doesn't have any draenei features. She could also be a Mok'Nathal half-ogre, like Rexxar.
One of the more interesting theories is that since the only human who had contact with Draenor before the Dark Portal opened was Medivh, Medivh is Garona's father. Therefore, Garona would be part of Sargeras's grand plan to destroy the humans, which is why she suddenly killed Llane after becoming close to him. Other theories on her parentage involve time travel, and the absolutely hilarious idea that she's Thrall and Jaina's daughter, which definitely gets into kill-your-own-grandfather territory. Right now, it seems that her family origins are a mystery for a reason, and we'll probably find out at some point.
For more information: Wikipedia on Garona, WoWWiki on Garona, WoWWiki's discussion of Garona's parentage and timeline.