Well, the bare rules just talk about how there are major and minor quests, and how achieving them grants XP basically just like any other reward (generally equal to a monster of your level for a minor quest, or a full encounter of your level for a major quest). The reward is granted to the party, and treasure is also rewarded. It doesn't say EXACTLY how much of this should happen, but it generally seems like its intended to represent 10-20% of XP for any given level.A summary of 4e's procedures on player-authored quests, would be really appreciated, at this point.
I get it is a sort of stipulation, Player declares a goal, Gm sets a reward (or XP?) based on difficulty, but then, how actual play unfolds? The Gm sets up an adventure about it? An encounter, or skill challenge?
In terms of the overall role of quests, etc. DMG p102 has a section (part of Chapter 6, Adventures) which provides a considerable amount of information:
1. Quests are "the fundamental story framework of an adventure" - so 4e is supposed to be BASED AROUND quests as its core architecture!
2. A list of 'quest seeds' is provided. These basically list most of the fairly common adventure motifs that you find in D&D. This indicates that basic stuff like "we need to escape from the Orcs!" IS A QUEST. So XP should be getting doled out (and treasure) based on "just having adventures" effectively.
3. An adventure normally contains three 'quest seeds', which formulate the basic quest motif of the adventure. When fleshed out these three seeds should specify the parameters of the undertaking, like 'Slay the Dragon of Weldhelm Pond and bring back its treasure!'.
4. Each quest has a level, just like encounters, but normally this will be set to the expected level of the PCs at the time of quest completion. It could be somewhat higher if it is extra difficult.
5. There are some other miscellaneous 'rules' of quest design intended to point out elements like clear goals and such that will make them more effective. The upshot is, quests are an open thing, the players, and probably the PCs, know what their goals are and have some idea of how to achieve them, or at least know to look out for such.
The system then tells us that there are Major and Minor quests. A single major quest can define an adventure, while several minor quests can form subplots, etc. It then states that "Thinking in terms of quests helps focus the adventure solidly on where it belongs; on the player characters."
Finally there is the "Player-Designed Quests" bit, which is the last subsection in the whole section. It states that the GM should 'allow and even encourage' players to 'come up with their own quests'. The GM then assigns it a level, and is admonished to 'say yes'.
So, 4e never quite completely leaves the "GM is in charge" planet, explicitly, but it is pretty clear that in terms of how it should be properly played, that players are AT LEAST allowed to generate quests, and the GM should only veto ones that are outright breaking the established fiction or genre/milieu. In a game where the participants are playing in a Narrativist mode, this procedure is adequate to establish a pattern where the players address their character's concerns by designing quests, and the GM's job is limited to framing the encounters required to actualize them in accordance with the rest of the encounter building rules, and keeping in mind the advice on constructing adventures and campaigns where it applies. You can also play in a more traditional mode where now and then a player suggests/establishes through some action or detail of background a motivation that is then elevated to the rank of quest. This would be very close to the way 2e suggests XP should work in a general sense.
So we see that 4e isn't textually committed in an explicit way to Narrativist/Story Now kind of play, but it is carefully woven into the game at multiple points such that you could play a very player-focused and directed game with very little overarching GM direction on where it goes. As with various indy games the GM will still play the key role of actually establishing each scene's details and thus challenging the PCs. One area where 4e doesn't really delve much textually is in terms of focusing this sort of thing on dramatic needs arising out of PC personality factors and such. It is highly doable, a PC at level one even, has a lot of 'hooks' inherent in their race/class/theme/background/feats/skills/power selections alone, but beyond the 'candy' of keywords and a lot of suggestive background bits that are dropped around that part is really left largely unsaid.