Your options are as such: (Variability depends on tabard worn(if), number of guildies and event selected)
Opt. 1-Arena 2's, 3's, 5's etc. w/ or w/o guild mates gains guild rep, results may vary (best suggestions for speedy gains: wear tabard if available,bring a guildie, win :))
Opt. 2- Questing (Including dailies) w/ or w/o wow guild
mates gains rep per quest, you can also grind low lvl quest if your into that sorta thing :/, results may vary
Opt. 3- Rated BG's w/ or w/o guild mates gains guild rep, results may vary
Opt. 4- Dungeons (HC's) (Including dungeon quest) w or w/o guild mate gains guild rep, results may vary
If you are a bad Arena player I would suggest not doing it.....as I would suggest the same if you are bad at HC's BG's and questing etc.
Its quite obvious by the high volume of completely different replies available that, the easiest way to gain guild rep is purely a matter of what you are capable of doing to EARN it. In other words you will only gain your rep as fast as you can farm it or until you cap out. If you find your self in a position where you are capping out weekly rep you should reach your desired rep lvl very shortly. Choose one of your options listed above, try it out and good luck :).