It's hard to summarize the setting of A Game of Thrones, in part because it's a totally imaginary world with a lot of detail, and also because the action of the novel takes place all over this world. Like seriously, all over. But here are a few helpful hints to start you on your analysis.
Don't get too hung up on geography. If you want to know where Winterfell is, just look at the map at the beginning of the book: Winterfell is far north, the closest family castle to the Wall. (That means the Stark family is closest to the Wall.) And this wall? It's the boundary between the "civilized" Seven Kingdoms and the uncharted north. Because of its geographic placement, the Stark family is on the front lines of this war against winter. (Spoiler alert: if you ever fight a season, the season will probably win.)
Bottom line: don't get hung up on all the geographic nuances of the world. All you need to know is that there's one continent in the west (named Westeros, where the Seven Kingdoms are) and one continent in the east (which has no name in this book). Oh, and there are other continents out there – it's a big world, after all.
The world is big and there are a lot of places, but there are only a few types of place. For instance, the Starks live at Winterfell, the Tullys at Riverrun, the Lannisters at Casterly Rock (which we don't see), etc.: these are all castles. Life in a castle is pretty much the same wherever you are: the noble family has a lot of servants to do all the work, while the more important people do the political and other jobs that remain. (In its own way, that's also the situation in the Night's Watch at Castle Black: the young boys do a lot of the nitty-gritty stuff and the older, more important people spend more time on planning and politics.)
So castle life is pretty much the same, but it's very different than, say, life in a war camp (like Tywin Lannister's camp where the Old Crossroads Inn used to be) or life as a nomadic horse-rider. Sure, the Dothraki have a city (Vaes Dothrak), but they only go there to visit. The rest of the Dothraki life takes place outside, in the wide plains of the Dothraki Sea (which isn't a sea at all, just a giant grassland plain). In fact, you could probably make some pretty interesting comparisons between the Dothraki customs and where they live and the Westerosi customs and where they live.
For instance, the Dothraki believe that the important things in a man's life need to take place outside; so when Daenerys goes to seduce Khal Drogo, she brings him outside, where everyone can see. (Hey, whatever works for you.) By contrast, the people of Westeros live in cities with solid walls, so a lot of important stuff happens secretly, where no one can see them. (Well, no one but Varys.) So, maybe their different styles of architecture tell us something significant about these different people and how they feel about secrets.
As we said, you shouldn't stress out about the geography in A Game of Thrones. Instead, spend your time stressing about the different cultures that we meet in this book. The people of the Seven Kingdoms are vaguely like medieval Europeans: they have knights and castles and marriages that are really political/economic contracts. Meanwhile, the Mountain Clansmen do things differently--they have chieftains and war captains, but they also make many decisions democratically. (They kind of remind us of a cross between Scottish highlanders and Norse Vikings.) And in the Dothraki tribes, the ruler is the strongest guy, not the kid who just happens to be descended from the strongest guy.
These many different cultures may be the most confusing element of this setting. After all, it's not like Martin can draw a map of cultural customs. (What would that even look like? Oh man, now that we're thinking about it, that sounds awesome: you could see where customs came from and how they spread. Go do that.)
The cultures and customs are central to the plot because they affect what people do and think. For example, the people of the Seven Kingdoms follow primogeniture, which means that the first kid gets everything and younger sons have to make it on their own elsewhere. (Which is why Eddard is Lord Stark and Benjen is in the Night's Watch.) Bottom line: it's pretty important to understand the customs of this world in order to understand the characters and plot.
Luckily, Martin has one major trick for helping us through this, which is that he often throws outsiders or newbies into the mix and has them think about the differences. For instance, Daenerys is obviously a newbie in the Dothraki way of life, so she has lots of servants to explain things to her. (Our favorite is probably Jorah Mormont, since he explains both the Dothraki way of life and the Seven Kingdoms way of life to Daenerys. Thanks, Jorah.) Similarly, Jon is new to the Night's Watch; and Arya and Sansa are new to life at court in King's Landing. (Note that we don't get Robert's POV since he's mostly at home – he's not an outsider at all. And anyway, his chapters would just be about drinking and sleeping around.)
One of our favorite examples of this might be Catelyn Stark. See, Catelyn lives in the north with the Starks, but she's originally from the south. So she looks around at the northern world (in the first few chapters) and she tells us a lot about it because it's still foreign to her. Do you want to know about the difference between the Faith that's worshipped in the south and the old gods that are worshipped in the north? Read Catelyn's first chapter.
Martin uses a similar trick to get us to understand the history, which can be very confusing. That is, Martin could sit us down and give us a huge chunk of a history lesson. But instead, he shows us bits and pieces of the history of this world through people's thoughts and opinions (and sometimes through their dialogue as well).
For instance, why does Eddard Stark dislike Jaime Lannister? Well, Eddard never told Robert this before, but when Robert was recovering from a wound he got when he crushed the Targaryen army at the Trident, Eddard raced ahead to King's Landing where he found… And the story goes on, telling us how Robert won the battle and what the Lannisters did during the war. (Check it out if you need a refresher: 13 Eddard 2.60.) This is history that Martin could have put anywhere in the book, but he uses his characters to convey the information. That is, Eddard needs to tell Robert something, so we get a tiny history lesson.
Over the course of seventy-three chapters, these tiny history lessons can build up into a large history lesson. Here's an example: Valyrian steel: 2 Bran 1 tells us that Eddard has a Valyrian steel sword and that it was forged with magic (ooh); 3 Catelyn 1 tells us that Valyria was a place that has since been destroyed by some "doom" – which is one reason why Valyrian steel is so precious, because they can't make it anymore; and then, 4 Daenerys 1 tells us that the Targaryens were originally from Valyria. In this way, Martin builds up an idea of the world by slowly building up the story of Valyria and Valyrian steel.
These tiny history lessons are spread all over this book, like a fine shmear of cream cheese on an 800-page bagel. Of course, it can be confusing to follow, which is why Martin gives us another cheat sheet: in the Appendix, he gives us a little timeline of the Targaryen conquest of Westeros.
In case you need a refresher, the major historical moments are as follows
If you're interested in all the details of the setting, check out any of the fan sites, which go into great detail on this. (Just be careful of spoilers. There are lots of secrets in this series, and if you haven't read all the books, you might be in for a shock.)
(Also, if you want to know more about the setting, check out the character pages: almost every character in Martin's book tells us one thing about this world, from the lowliest Night's Watch guard to the highest, um, king.)