I have never read the books, but was pretty much able to follow the characters without difficulty and also gleen some pretty important background as well.
First Ned Stark and King Robert are old friends. Ned's dead sister was Robert's fiancee and was killed in some way by one of the Targaryens (the blonds). This death caused the two along with Jon Arryn, the dead "hand of the King" to organize an overthrow of the Targaryens and also kill most of them. To secure his position Robert married a Lannister a politically powerful family in the capitol.
Ned Stark goes off the protect and rule the North, but also to escape the snake pit of the capitol city.
Ned is now a good husband and father but he has a Bastard son, most likely before he was married. However he looks after the boy as best he can. Bastardy seems to be a mildy important status thing in this society. I mean everyone knows he's a bastard and who's he is, but Ned's wife doesn't seem to mind him teaching her children, and he appears to have some useful job. But he is excluded from the party.
Anyone that has read the books care to comment on my accuracy so far?