Guild quests are the bread and butter of the game. Although you can improve your rep with the Guilds indirectly by completing quests for other factions, the gain is slow and very random (alliances shift at midnight each day).
Each guildhall has a questgiver to test your mettle. A problem reported by some players revolves around being unable to report back after completing a quest (the dialogue launches a new quest rather than closing the old one). The solution is to always use the "Get Quest" button rather than the "Talk" button. When you "Talk" to the questgiver, you are dipping into the Merchant/Inkeeper pool of quests. When you use the "Get Quest" button, you are dipping into the pool of Guild quests.
There is no penalty for refusing a quest, so you can keep asking for a quest until you get one that you want. As with other factions in the game, successful completion of a quest will usually raise your reputation with that faction by 5 points (there are a few quests that will raise it by 10) and failure will reduce it by 2 points. Beware of quests that reduce your rep with factions you need.