Step One: Keep the same cast
TV shows are popular because people bond/become interested in the main character and their supporting cast. If you were to do a different protagonist every season (e.g. DA:O is season 1, DA2 is season 2, etc) it wouldn't work. So either cut Hawke and the Inquisitor, or cut the Warden and backdate one of them to be the (non-Warden) protagonist. Since DA:O was the one with the "pilot pick-up", lets go with the Warden.
Step Two: Compress the time frame
DA, to date, has covered 14 years in game. That's obviously too long, unless you want to try and use make-up on your actors to make them age appropriate. Make each game story take place over roughly one in-universe year, and roll Awakening into DA2.
Step Three: The Warden can never win
All three games basically involve a plucky nobody challenging the powers that be, winning, and then gaining power and influence. That works on a game by game basis, but screws up serialised story-telling (as Bioware realised by exiling the Warden and the Champion from their homes). So the Warden does not become Warden Commander, or Viscount, or even the Inquisitor (or queen, which she couldn't do anyway because she's an elf). She remains a heroic outsider working against a corrupt or obstructionist system.
Step Four: Keep the supporting cast small
The companions should be capped at six at the most. More than that and the cast feels unwieldy, and don't have enough of an opportunity to play off each other. My choices would be Alistair, Leliana, Morrigan, Sten (proud warrior race guy) and Oghren (comic relief). Replace Oghren with Varric for season 2, and have Sten be made Tal Vashoth against his will (perhaps as a result of disagreements with the Arishok in season 2). Any other companions become recurring characters or special guest stars.
Also, write an escape hatch into each character's story in case the actor quits the show. Morrigan goes to Orlais, Leliana goes to work for Justinia, etc. Replace them with other companions if that happens (eg Dorian or Merril for Morrigan).
Step Five: Respect Your Protagonist
In this scenario the Warden, the main character and anchor of the show, is a woman from a disenfranchised minority group. You have to take that into account be true to the experience and outlook of such a character. Give her political views on alienages and militant Dalish clans. Don't let it overtake the whole character, but nor should you ignore that stuff.
Step Six: Love Triangle
Have an ongoing subplot involving potential romance between the Warden and Alistair, the Warden and Leliana, and possibly Leliana and Alistair (as is reflected in the Darkspawn Chronicles). "Will they, won't they" and "who should x be with?" are tried and true ways of generating audience interest. It would also be an interesting way of exploring the elf-human dynamic (Alistair's mother is an elf, Leliana is fairly ignorant of Dalish ways, etc). My preference would be for the Warden and Leliana to become involved, and for that to happen before the end of season, as that would add more drama to the story.
Step Seven: The Plot
Season 1 is DA:O, with a planned twelve (hour long) episode season. Tagline for the show is "What does it take to save the world?" Each treaty takes two episodes to resolve, with a two hour pilot and a two hour finale. Like the game, the goal is to stop the Blight but the primary antagonist is Loghain, who keeps trying to kill the Warden. Resolve the treaties by having the Warden make moral compromises (Bhelen is king, Branka kept the anvil, Zathrian is unwilling to die but the Warden kills him anyway, Irving let Uldredd operate as a means of strengthening the Circle, etc).
Have the Dark Ritual come up before the Landsmeet. Have Alistair do the DR as a means of saving the Warden who he has romantic feelings for; unbeknownst to him, the Warden and Leliana have become lovers. Then at the Landsmeet the Warden spares Loghain in order to ensure his forces join her own to combat the Blight. Alistair is outraged at this betrayal and leaves for Kirkwall (where he'll be re-recruited in season 2). Anora becomes queen. The Blight is defeated (in an awesome battle sequence) and the Warden is named Hero of Ferelden, while she privately reflects on the cost of victory. Final scene is a teaser of the Architect.
Season 2 covers the events of Awakening and DA2 and has a villain of the week flavor, with each villain (the Mother, Duke Prosper, the Arishok, Meredith and Orsino) taking two episodes to deal with, and all being manipulated by a shadowy unknown figure the audience is led to believe is the Architect. The reveal is that this was actually Anders all along, who the Warden met and befriended in episode 1, and who orchestrated events to start the mage rebellion. Anders dies, but not before starting the war. Season three teaser is of Corypheus.
Season 3 is DA:I, with Cassandra being Inquisitor and eventual Divine, and the Warden and crew being her primary agents.