You have to talk to either Bowen Brant (Ten-Towns faction) or Anara the Cerulean (Arcane Brotherhood faction). Some (one?) of the quests available at one point are affected by which one you're signed up with.
So, first you get a quest from Knox (I think). Then you talk to the guy in the caravan behind the market. Then you'll do whatever the intro stuff is. Once you get there, you do like nunya said and get a contract for one of the factions. You don't have to always do the same faction - you shouldn't actually since there are achievements for both and the quests are slightly different - but you can finish the whole campaign without ever going with different factions. The contracts expire after a day, so you'll need to get a new one each time you go do dailies. Once you have a contract and have picked up the dailies from all the various NPCs - you'll be good to go.
Also, the most important quests to do every day are the Demon Hunting quest and the quest given by Anara or Bowen (depending on your faction). Those are the only ones that award Caer-Konig Reputation. You cannot get Caer-Konig Reputation by turning in Genie's Gifts, either; those will only give you Konig Coin, Dwarven Gold, and Tears of Auril (or whatever the blue teardrop looking thing is called). All the achievements and boons in this campaign are gated behind your Caer-Konig Reputation. If you can do those quests I've mentioned daily, then you'll progress quickly through the campaign. (I've been lazy on my paladin and he's getting there about 30 or 40 Caer-Konig Reputation per week. It's the best I can manage because I get bored.)
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Sekhmet@kvetchus_
Guilds: Greycloaks, Blackcloaks, Whitecloaks, Goldcloaks, Browncloaks, Spiritcloaks, Bluecloaks, Silvercloaks, Black Dawn
Tredecim: The Cloak Alliance