How do you gain Guild Reputation?

Anytime you do something that awards Guild Experience (or would, were your guild not at the cap), you'll earn Guild Reputation, up to the cap. Guild Rep gained is equal to guild XP generated/365 (Guild XP is 1/4th of the XP your character gains, or would gain if at level cap).

Phrased another way:

Guild Rep = Experience/1460

If you want to gain guild rep fast, the best way to do it is far and away by running Heroic 5 mans. It's fairly easy to cap for the week after just a few runs.

Reputation from a 25 man Raid Boss on normal mode is somewhere between 56 and 58. The exact fractional value is, unfortunately impossible to determine due to the way WoW displays fractional rep gains. (that is, it doesn't, but it does track them.)

The weekly cap on reputation, as pointed out by Raven is 3500 reputation. This cap increases to account for any +rep gain modifiers such as the Human 'Diplomacy' racial trait, or the 'Mr. Popularity' guild perk (both ranks). (i.e. for a Human in a Level 12 guild, the weekly cap is 4200).

I found this table on WoWpedia with rep-cap information

The following is a table of the weekly guild reputation cap for various states: