Sansa is the oldest daughter of Eddard and Catelyn Stark; Sansa is younger than Robb Stark but older than Arya, Bran, and Rickon. (She's also younger than Jon Snow, but she makes sure to let everyone know that he's only her half-brother.) Sansa is betrothed to marry Prince Joffrey; that means she'll be queen one day. She goes down to King's Landing when Eddard is named Hand of the King and everything goes well. Oh, except that Cersei takes over and Sansa is taken hostage, where she learns that Joffrey is a monster. Boo.
All you need to know about Sansa in this book is that she has a direwolf – a giant, monstrous wolf, a half-mythological monster, a killing machine – and she names it Lady. You get the point? Or how about this: the wolves take on the personalities of their owners (16 Sansa 1.35), and Lady is "the prettiest, the most gentle and trusting" wolf (17 Eddard 3.64). Yep, that's a pretty fair description of Sansa.
Sansa wants to be a great lady and a lady always remembers her courtesies. She pictures herself as the beautiful heroine of a romance, so her major goal is to fit in with that ideal of a woman. (See "Gender" for more on that.) In fact, all Sansa wants is "for things to be nice and pretty, the way they were in the songs" (16 Sansa 1.38).
… In an Unromantic Book
Sansa is incredibly unprepared for the real world (well, the real world of A Game of Thrones), which is incredibly frustrating. Because Sansa gets six POV chapters, we get to see her thoughts pretty clearly, and they definitely don't match up with reality. But what's so wrong about wanting everything to be nice and pretty? We want things to be nice and pretty, too! The real problem is that Sansa doesn't seem to be able to tell the difference between the way things are and the way they should be; because she wants her life to be romantic, she projects all these romantic clichés onto the world. (To be fair, though, isn't that kind of Eddard's problem, too? He wants people to act honorably, but they don't.)
But what really gets us is that she takes this romantic urge so far as to betray her father by informing Cersei Lannister of their plans to leave (52 Sansa 4.50). Why? Because Sansa has this crazy notion in her head that she loves Joffrey. Luckily Sansa snaps out of that craziness, though she only seems to learn who Joffrey really is (a monster) after her father is beheaded. That's a pretty high price to pay for a lesson. (It should make us all appreciate our teachers a bit more.)
So, in the end, Sansa does learn the lesson that Lord Petyr told her about: "Life is not a song, sweetling. You may learn that one day to your sorrow" (45 Sansa 3.9).
Reality check: Sansa is eleven (5 Eddard 1.71). So maybe we should cut her some slack. Still, sometimes she reminds us of a kid at school who only cares about what's popular. This would be okay if she didn't want everyone else to care about what's popular, too. (See, for instance, how Sansa and Arya never can agree on what's fun. Or how Sansa's friend Jeyne calls Arya "Horseface" and Sansa never tells Jeyne to stop. It's almost like being cool is more important to Sansa than her family.)
Minor Characters Connected to Sansa
The daughter of Vayon Poole, Jeyne is about Sansa's age. Like Sansa, Jeyne is interested in beauty and romance. Needless to say, things probably don't turn out so well for her: after Cersei takes over (and her father is killed), Petyr says he'll find a place for Jeyne. Who knows what that means.
(Also, while the spelling is strange, notice that Jeyne sounds pretty much like Jane. This is another of Martin's strange-but-not-so-strange names.)