To give a canonical beginning to the game's story arc is difficult, because there are six origin stories you can pick from which shape your character's background and the reactions of other characters to you. Easier, then, to simply begin with the beginning of the lore.
"And so is the Golden City blackened/With each step you take in my Hall./Marvel at perfection, for it is fleeting./You have brought Sin to Heaven/And doom upon all the world."
- Canticle of Threnodies 8:13
The first race to rule much of Thedas (the continent on which it is set) was the Elves, who were at the time immortal. Their nation, Elvenhan, was ruled from the great city Arlathan somewhere within what later became known as Imperial space. At some point throughout their history, they met with the Magisters of the Tevinter Imperium (both the leaders of the Imperium, and powerful mages), and began to lose their immortality around this time. Although lost to history, it is suspected that the Magisters are to blame for this act. The Elves began to isolate themselves around this time, but the Imperium wages a war against Elvenhan, and enslaved the Elves. To this day, it remains legal in what little is left of Tevinter to sell elves into slavery, or for elves to sell themselves into slavery to provide for their families.
The Imperium ends up ruling more-or-less all of Thedas. Four hundred years before the Chantry Ages began, a group of Magisters attempted to physically enter and perhaps conquer the Fade (the Fade being all at once the spirit realm where you go when you dream, where you go when you die, and the source of all magical power. Demons and spirits live in the Fade, lurking in the hope of finding a way to cross the Veil into the mortal realm). They succeeded in entering the Fade, even getting into the Golden City of the Maker (basically this amounts to Heaven). When beings still living entered the Golden City, it was corrupted, transforming into the Black City. The Magisters who committed this prideful sin became the first of the Darkspawn. Upon their return, they tainted many of their peoples (darkspawn can taint through contact with their blood, or by general exposure to the malevolent aura that surrounds hordes of them), and were forced to flee the light of the sun. They were driven underground to dwell in the Dwarven Deep Roads, whereupon they cut a massive swath into the Dwarven kingdoms underground.
Shortly after, the Darkspawn returned to the surface in Tevinter, led by an Archdemon (essentially what happens when a great high dragon is tainted). This was the First Blight. It essentially annihilated most of the Imperial strength. The Grey Wardens, created by deliberately ingesting the blood of darkspawn (making them immune to its taint, allowing them to sense darkspawn, but also shortening their lifespan considerably), were created to help fight back this darkness. The Blight was eventually defeated and driven back underground upon the felling of the Archdemon. The post-war weakness of Tevinter allowed the Prophetess Andraste - later taken by the Maker as His bride - to lead a barbarian army to break the back of the Imperium's strength. Andaste is able to cut a huge swath into Imperial territory, freeing massive expanses of their southern lands from Imperial rule, before she's finally killed by a jealous general within her own rank. The Imperium never recovered from her many victories.
Following the shrinking of the Imperium, several nations arose from their ashes. Many elves, freed from Imperial tyranny, forged a new nation in a land they called the Dales. They built a new city, and all was well for 170 years. Their doom was spelt by the founding of the Chantry of Andraste (essentially Dragon Age's analogue to the Christian Church - it calls for everyone to worship the Maker, and prophecises that the Maker will once more watch over them, and that the Golden City will be restored, if everyone on the planet believes in the Maker and calls out His name), which called an Exalted March (crusade) and conquered the Dales for the Empire of Orlais, one of the new nations that arose after the crippling of the Tevinters. The Orlesians also subjugated many human settlements. Most Elves therefore live as second-class citizens in Alienages (ghettos) across human lands, living in poverty and only able to get jobs as servants. Some free clans exist in the forests of the world, searching for ancient Elven technologies and relics that they believe will lead them to a new nation. These are referred to as the Dalish Elves.
The Orlesian Empire is the most powerful and largest nation in Thedas, though it shrank considerably when King Maric of Ferelden liberated his nation from the Orlesians thirty years ago. In this, he had help from Flemeth, Witch of the Wilds.
Now, a new Blight - the Fifth Blight - has begun. None have ever erupted as far north as Ferelden before, and this far north the Grey Wardens are not well-liked. King Cailan, son of Maric, has died on the battlefield facing darkspawn, betrayed by one of his two Teyrns - Teyrn Loghain Mac Tir of Gwaren (the major baron-lords of Ferelden). The other Teyrn, Teyrn Bryce Cousland of Highever, was betrayed to his death, and his castle sacked, by one of Loghain's allies, Arl (minor lord) Howe. Cousland's son and his trusty Mabari Hound escaped this ruin and were recruited into Grey Warden service in light of this new Blight, and was one of two survivors of the battle Cailan died in, the other being Alistair. They survived by fleeing into the Kocari Wilds, where they met Flemeth and her daughter Morrigan. Flemeth ordered Morrigan to travel with the pair, sensing that they needed all the help they could get.
Wow, that was a confusing summary wasn't it?
For more detailed and useful and effective information on the events, peoples and concepts, check out The Dragon Age Wiki.
