Leia was born on Polis Massa, grew up on Alderaan, and kicked ass on every planet she set foot on.
Leia's mother (I mean her real mother) gave birth to Leia and her twin brother Luke while dying of a "broken heart" on Polis Massa. Obi-Wan assisted while Yoda and Bail Organa watched and cringed. Birthing droids did most of the work. Luke was born first, but Leia was stronger and cried far less. Bail's wife Breha couldn't have kids, so he jumped at the chance to bring a healthy baby home and raise it. Of course Bail didn't even stop to think, "Wait...this is Darth Vader's kid...might be a bit of a handful," nor did he check with his wife first. That's just how Bail rolled.
Life On Alderaan
Leia grew up on Alderaan, causing many headaches for her adoptive father. Bail didn't have much interest in actually raising the foundling, since he was busy being an important senator and all. After his wife died, he mostly just let the servants handle everything. He changed his mind, however, when Leia began showing signs that she was not an idiot. Bail used his power as ruler of Alderaan to appoint his adopted daughter to the Imperial Senate. Even though Leia was very young, Bail figured she was qualified enough, since the Imperial Senate really didn't have any power anyway.
Bail was also a key and active figure in the Rebel Alliance. He figured Leia would be a useful member as well, so he brought her onboard. Mostly she was to use her role as senator to justify mercy missions and press junkets in places where rebel support was high. She became a highly respected and visible member of the Alliance- mostly because she was way better looking than Mon Mothma, and was less likely to offend people with inappropriate comments.
A Nude Hope
Eventually, Bail decided to set things in motion, so he sent Leia to find Obi-Wan Kenobi. On her way there she was captured by her dad, who didn't know that he was her dad, and sentenced to death after being forced to watch Alderaan get blowed up. Fortunately, she was rescued by her brother and a scoundrel she found way do-able. She still ended up getting the credit for delivering the stolen plans to the Death Star, which was destroyed during a tense battle, while she hung out and watched it on a map with some old guys and C-3PO.
The Empire Strikes in the Back
The Rebels escaped Yavin and went to an ice planet. While there, she began to realize that Han totally wanted her, but she decided to use that to manipulate him by instead showing affection for the guy that she strongly suspected to be her brother. When everyone evacuated, she was stuck with Han in a ship that conveniently had no Hyperdrive. They escaped to Bespin, where Lando Calrissian lavished her with expensive dresses that just happened to have been left in his bedroom at various times. Leia's enjoyment was short-lived however, when Vader showed up and started playing macho head games with Han. Leia realized that she might as well make her feelings for Han clear so that he wouldn't spend all that time encased in Carbonite worried that she was going to start fooling around with Luke while he was gone. Though Vader attempted to take Leia and Chewbacca prisoner, Lando helped her escape and she was able to rejoin her Rebel associates.
Return of the... Stuff
Leia, Lando, Luke, and Chewbacca hatched a plan to rescue Han, which involved lots of disguises and stuff. It didn't really work. Instead Leia ended up chained to Jabba the Hutt. This turned out to be only a minor setback, and possibly a benefit, since she used the chain to strangle him to death while her brother murdered a whole lot of people. After that, Leia volunteered to go on some dangerous mission to shut down a shield generator or something like that. Mostly she wanted to hang out with Han. After being separated from her group, she was made princess of the teddy bears, who happened to have a human-sized dress for some reason. Eventually, she hooked back up with the others and participated in the back-door assault on the Imperial complex. The team was able to bring down the shield and the Rebel assault on the Death Star went pretty well after that.
Leia was instrumental in setting up the New Republic. And people had a glad.Han and Leia got married and had some kids. At least one of them was a shithead.