The *only* quick way to get resources is to buy them from the AH. Having said that, I don't recommend doing that unless you're a wealthy veteran, as buying your way though a trade skill is expensive.
In the case of Dwarf-Iron, mining in the Trollshaws, Mistys, and Angmar are your only options that I can recall. It can be a real pain to do in Angmar unless you're high enough in level to avoid aggro, but can also be well worth it as it's an under-utilized area for resources (at least on the Landroval server).
There is a third option; there are vendors that will essentially "sell" you resources every six hours. The ore seller is located in front of the Silver Deep Mine in Thorin's Gate (NE corner) and is called the "mine foreman." In his purchasable inventory are documents which basically act as requisition orders, price based on the tier of ore you want (I think the most expensive is 40s). You purchase the "order" and in 6 hours come back to collect a key from a nearby NPC. Use this key to open the appropriate chest behind the foreman to collect your ore. This really isn't nearly as effective as actually mining the ore yourself since you receive less than a dozen pieces of ore, but is sometimes the only way to get higher tiers of ore if you're too low of a level to get it yourself.
Edited, Oct 26th 2009 7:58am by Gladestrider