Quickest way to obtain astral diamonds

The Auction House is potentially the best way to gain Astra Diamonds. However, like anything that requires human interaction, there isn't assured success in selling the items. That said, the dailies you get are your best bet.

It should also be noted that there is a limit of 24k AD that you can refine each day. So no matter how many dailies you do, you can still only gain 24k AD from said dailies (as all of the rewarded diamonds for dailies are "rough" and require refining").

There are a lot of ways to get AD, but most of them offer small amounts (for instance, Foundry tips).

Crafting and selling on the AH.

Shirts and Pants don't drop, they need to be crafted. Most people don't know this. I've been monopolizing high level shirts/pants for TR and CW for the past week.

My AD is over 4 mil, and I haven't done dailies since level 20ish.

Also, using Gateway, you don't even need to be online to do this. I expect 10% of your sales, now. ;)