There seems to be a lot of confusion about how the new Guild systems work, so I thought I'd throw this together to provide some information.
Blizzard has made a blog post discussing some of the new Guild System aspects, you can find it here:
Guild XP is what you need to level up your guild. You can earn Guild XP a number of ways, provided you're not already at the daily Guild XP cap. It takes 16,580,000 (16.58 Million) XP to reach Guild Lvl 2. Reaching Guild lvl 25 will take a total of somewhere around 850 Million XP (wowpedia says 845,670k, but when I add up their numbers I end up with 855,690k).
The Daily Guild XP Cap is 6,240,000 XP (that's 6.24 Million XP) per day.
The cap is there to prevent Mega Guilds from reaching Guild Level 25 insanely fast. It also helps level the playing field somewhat between small, medium, and large guilds, though larger guilds may still end up leveling somewhat faster than small guilds as small guilds may not be able to hit the cap reliably.
It's also there to prevent people feeling or being compelled to play as close to 24/7 to reach max level as quickly as possible. For the purposes of this Guide, a Small Guild = 10-25 Accounts, Medium 25-50 Accounts, Large 50+ Accounts.
FAQ: Guild Levels
How long will it take to reach max level?
Patch 4.0.6 removed the GXP cap once level 23 is attained. This reduces the potential required time to guild level cap by a significant, yet variable, amount. A guild could level cap in as little as 18 weeks now.
What Perks and Rewards are unlocked at what Guild Levels?
See the WoWHead link at the bottom of this post.
Earning Guild XP
GXP can be earned via questing, running dungeons and raids in a guild group, pvp (in a guild group) and completing guild challenges.
Questing: 25% of Quest XP is earned as Guild XP.
Dungeoning (5 mans): A group can earn guild xp as follows:
3 Guild Members: 50% GXP (18.6k for heroic bosses)
4 Guild Members: 100% GXP (37.2k for hbs)
5 Guild Members: 125% GXP (46.5k for hbs)
Raids: 80% of raid comprised of guild members. (TBC and prior raids are all considered 10 man raids for guild group credit calculations.)
Winning Rated BGs with a Guild Group (amount dramatically increased in 4.1)
Winning Arena with a Guild Group (100% of team members in same guild)
Battleground Wins in Brackets up to Lvl 80.
Honor kills in the field.
These challenges are found on the info pane of the guild interface. Guild Challenge GXP is awarded separately from the GXP cap (and pushes the cap for the current day higher).
Complete 7 Guild Group Dungeon Runs
Kill 1 Level Appropriate Raid Boss
Win 3 Rated Battlegrounds
FAQ: Guild XP
How much GXP is earned per boss/dungeon?
The full list is posted in this thread, with all credit to the creator of the thread and contributing posters:
How much GXP does it take to reach each level?
See the WoWPedia link.
Why is there a cap?
The cap is a gating mechanic, just like you have a cap on the number of dailies you can do in a day, just like ICC was realized one wing at a time.
Why is the GXP cap so low? I feel like I can't contribute to my guild's progress because it gets maxed out in an hour or so every morning before I log on.
The amount of GXP required to level and the cap is low to allow smaller guilds the same amount of opportunity to level as larger guilds. This was likely a much easier and less technically difficult system to implement than one that would require more GXP for a guild to level based on the number of active members in the guild, or limiting contribution to only the guild's top 20 contributors. You can still contribute to your guild's progress by helping to work towards Guild Achievements (like fishing up 10000 fish, cooking 5000 cata recipes, etc).
What determines the daily cap of how much guild XP you can get? Does having more members increase the cap?
The cap is a static 6,240,000 (6.24 Million) XP per day. Having more members does not increase the cap, or the amount of XP required to level.
I believe I read somewhere that GXP gained by players while the daily GXP limit has been met is automatically applied to the next available day, is this correct?
No, GXP earned after the cap is lost, not saved.