1/3 How on earth do the titles and styles of the Westeros nobility work? I am so confused, and part of that is probably because I know a lot about how titles and styles work in the British peerage (where Lady Catelyn and Lady Stark signify VERY different things). But I can’t make sense of it in AOIAF/GOT Sometimes people are called Lord first name, sometimes Lord last name, sometimes Lord first name last name. Children seem to be addressed by the same title as their parents (Lord and Lady).

2/3 And people of vastly different ranks seem to have the same title (Ned might be Hand of the King, Warden of the North, and so on, but he and Littlefinger and someone like Roose Bolton or Walder Frey, who are of different ranks and come from different places are all Lord of _blank_). The bastard of minor lord (albeit one with a high office) is addressed as Lady Alayne, but the bastard of the Warden of North is mockingly called Lord Snow.

3/3 And then you have Ser, and presumably some people who are called Lord also are knights, so how does that work? Titles seem to follow people to the Wall, but no to the Citadel or the Seven. I know sometimes people look to the historical time periods Westeros is based on for this kind of thing, but even that gets me at a loss, like Westeros clearly has the title of Princess which is a much later term. I just can’t figure it out. What am I missing?

Oh man, titles are such a tricky subject. 

The thing to start with is that GRRM deliberately went with a simpler form of noble titles because he didn’t want to have to keep track of which outranked or had precedence over the other, although this creates some difficulties.

1. The way GRRM seems to use it, Lady Catelyn vs. Lady Stark is about familiarity and formality. Lady Catelyn suggests you know the person and are being familiar with them, Lady Stark suggests you don’t know them well and are being formal, Lady Catelyn Stark suggests that plus you’re being very formal and/or precise. 
2. Ranks tend to be indicated by additional titles: Lord Paramount of X, Warden of X, Lord of X Castle, etc. 
1. As for children, this to me is similar to how smallfolk members of the Small Council are called Lords out of courtesy as opposed to by right. 
2. Lord Snow is an insult by way of exaggerated courtesy.
3. In pretty much all cases, you address someone by their highest rank, so a lord who is also a knight (and most sothron lords would have been knighted at some point) is called Lord. (There’s a bit of confusion over the Darrys, but this may be a case of Early Installment Weirdness) 
1. As for the Night’s Watch, the title of “Ser” definitely carries over, because the oath requires you to abjure holding land. Don’t think there are cases of any Lord who isn’t a Lord Commander, tho.
2. As for the Citadel, maesters swear “sacred vows, to hold no lands or lordships.” I don’t know of any case of a knight becoming a maester, but presumably the same principle that applies to the Night’s Watch applies to them. OTOH, Aemon stopped becoming a Prince after he became a Maester although it’s possible that A. at the point he did that he was a “Prince of” something, which would indicate lordship or B. that as Aemon saw it, he stopped being a Prince when he ceased to be a Targaryen, since maesters give up their family names, which the Night’s Watch doesn’t.
3. We don’t know the rules for the Seven, although presumably it’s the same as the Citadel.
4. Pre-Targaryen monarchies outside of Dorne do not seem to have used the style of prince or princess, as we see with Argilac’s daughter being referred to as “Lady Argella” and not “Princess Argella.” The Targaryens started using the style somewhat belatedly, because for some reason people started using the Dornish style. 

@goodqueenaly, any thoughts?