What's the best way to teach/learn the Game of Thrones board game for people who haven't played before?
This is a very general question and really depends on who you're playing with (and how they're feeling at the time).

Playing any new board game with a group of new players can be a daunting task, and a lot of players are reluctant to listen to a rules explanation for an hour before you start.

If nobody knows the rules then, unless the game is simple, it's likely (as you experienced) that the group will give up. Unless you have enough rulebooks for everybody, or a really interested group, having one person read the rules in front of everyone is a bad idea. As you mentioned, a better idea is to have someone take charge, and read enough of the rules in advance that they'll be able to set up and guide the learning.

It's fine for that player to follow along with the rulebook. A new player is a good facilitator, especially if everyone understands that they're still learning too. This helps avoid blame where you didn't give them all the options or explain all the rules in advance (and if you did they'd have stopped listening or given up!).

Set up the basic parts of the game and give a brief explanation of what the board means and how the game flows. Then you can go through phases in a bit more detail. Try to mention the various options without necessarily explaining the details (again, this helps avoid the "you didn't tell me that" issue).

Then finish setting up, getting the players to help out (e.g. "can you sort the cards into coloured decks, can you give each player a set of tokens, please?"). This helps everyone get a sense of the different parts used in the game and the names of those parts, which helps understand the rules as you go on.

Then, start playing the game, stepping through the options and details of what's going on. After a couple of rounds you can ask everyone if they understand, and offer the option of a restart. In my experience, most people will be fine to carry on unless they've accidentally devastated their own position, and resetting shouldn't be too difficult.

The most important part is for the group to accept that mistakes will be made. If you realise you were playing the game wrong, let people know about it and move on.

To reiterate the important points:


Have a player who's familiar enough with the rules to set up and help others understand the game. If nobody's played, someone should spend a half hour or so in advance.
Make sure everyone knows that it's a learning game, and that it'll be a bit of a muddle the first 1 or 2 plays.
Be ready to allow people to undo recent mistakes based on rules misunderstandings, or to stick with/change incorrect rules as you play.
Focus on getting everyone to understand what's going on rather than just picking easy options. Encourage the whole table to share good strategic advice with everyone, even their opponents, so that players can focus on strategy in later games.