I've got a lot of friends new to Dragon Age, and I feel like the first thing you should know is that the Dragon Age setting is a pretty direct roman a clef of European History. Some of it is hilariously obvious, but still - it helps to understand the setting if you know some history. No spoilers, just an analysis of the setting. Take the below map and Invert it and flip it. Par Vollen is North Africa and Ferelden and Orlais are Northern Europe. Go from there.
Orlais - France, in case the accents and the cheese didn't make it obvious. Its post-Renaissance, pre-Revolution Early Modern France.
Fereldan - Anglo-Saxon England, also fairly obvious with the accents and the wet, cold, English countryside.
The Chantry - Lady Catholics and Andraste is Lady Jesus. Andraste guide us.
Apostates/Rebel Mages - Mostly the atheistic, pagan representatives but really anyone that the Catholic church deemed a "heretic" during the Catholic Inquisition fits in here. Hey, Inquisition....WAIT I GET IT
Now for the more difficult ones...
The Free Marches - Nevarra is Prussia and the rest of the City States are basically Austria or a very loosely organized Holy Roman Empire. Kirkwall has a lot of similarities to independent Cologne. Trying to remain free of religious strife and failing, etc. You can call them America if you want a more modern analogue, and if you like being WRONG.
Anderfels - Eastern Europe under the Teutonic rule. I've heard this but the Anderfels don't feature a lot in the games so I've always lumped them in with The Free Marches....which makes sense in a Holy Roman Empire way.
Elves - They're Jewish. There's a bit of Romani, Native American, and Celtic in there depending on the region but basically they're Jewish. They either live in ghettos or are an ancient race of persecuted wanderers, come on! City Elves or Dalish, I say that's a pretty damn strong analogue.
Antiva - Venice with a mix of other Italian City States, but mostly its Venice. There's some Spain and Borgias Italy thrown in for good measure but Antiva = Venice.
Tevinter Emperium = Byzantine Empire. They've lost their former glory (Ancient Rome) and retreated into a smaller territory. They have their own version of The Chantry (Greek Orthodox) and are at war with The Qun. See below.
Qunari - They're The Moors (and more) of Islamic and European history, pretty much. Fierce warriors, conquerors, and dark-skinned tacticians that the rest of "Europe" sees as strange and barbaric with a bizarre religion and social system. "Qun" isn't exactly a stretch from "Qu'ran". Strict code of ethics, convert-die-slavery system, etc. Par Vollen is their main home, but they tend to spread over a lot of islands and coastal areas like Seheron.
Rivain - I think they're supposed to be Moorish Spain, but I really haven't gotten much into Rivain. But its the battlefield between Qunari and Andrastrians so it makes sense.