I'm reading the chapter on fleshing out the knight's family, but I'm wondering where you record all of this information. Particularly the rolls made regarding the Knight's grandfather and father, and their previous exploits. Furthermore, are these rolls generally made before a campaign, or do most wait and conduct this with the GM?

I generally do it as a group session at the start of the campaign, where the players roll each year together, and we get to see which of their fathers/grandfathers had the higher glory. Also, there's the possibility of describing how knights met each other.

Recording it: just on a sheet of paper, kept in the character folder. Once you're in play, you don't really need to refer back to it - any significant effects (like Hates and Fears) are there on the player-knight's sheet. Though if you do look back for plot hooks, the campaign will probably be richer for it.

Once a campaign is underway, that system gets less and less relevant, but I'll still use it one-on-one with players as they design replacement characters. After a while we skip it altogether. By then, players are usually playing the sons of characters knighted in 485 or later of course, and already have full family histories.