Originally Posted by Old Dude
Yup. Maybe this will help as a guide to who is related to who.
For about 300 years, Westeros (the England-like land where most of the action takes place) was ruled by the Targaryen dynasty - the so-called dragon kings. These folks were a little like the Egyptian Pharaohs and engaged in a lot of interbreeding. Marriages between brothers and sisters were common. (This practice did NOT extend to anyone else in the country.)
About 15 years before the story starts, the Targaryens were overthrown by a group of nobles. The leader of te rebellion was Robert Baratheon, who is now (the very fat and out of shape) King. (Baratheon also has a couple of brothers who haven't been introduced yet.)
The only surviving Targaryens were a brother and sister - and who were little more than infants at the time of the "usurpation." They've been bouncing around between various patrons on the continent ever since then. Theoretically, they have the primary claim on the throne and those who don't accept Baratheon's rule would like to see them returned. Obviously, their benefactors are hoping for various rewards and influence if this comes about. The sister, Daenerys, has just been married off to the continental equivalent of Ghengis Khan - with the hope that they'll eventually restore the Targaryens to the throne.
Among the noble families who assisted Baratheon in gaining the throne were the Lannisters, the Starks, the Tullys and the Arryns.
After the rebellion, there was a lot of intermarriage between these families to strengthen their alliances.
The head of the House of Lannister, Tywin, arranged a marriage between his daughter, Cersei, and King Robert. They have three kids, the oldest of whom is Joffrey. Cersei, as you know from episode 1, is having an incestuous affair with her twin brother Jaimie. Tyrion, the dwarf, is their younger brother.
The Tullys married off one of their daughters to Ned Stark. (Catelyn). The Starks have five kids. The other Tully daughter (Lysa) was married off to Jon Arryn. (They have one child - a boy). As the series begins, Jon Arryn (who was working as the Kings Right Hand Man) has died under suspicious circumstances. Lysa has fled back to the Tully castle and has written to her sister that she thinks Jon was murdered by the Lannister family.
Jon Snow is not a Stark. He is the bastard son of Ed Stark, who Ed allows to hang around.
The Theon kid we've been taking about is also temporarily residing with the Starks, but he's not directly related to them. He's from yet another noble family.
Anyway, that's for starters.