Light the Dragonfires!
Martin meets with Chancellor Ocato in the Elder Council Chamber (which is finally open). Even though your journal tell you that you should formally present him to the chancellor, Ocato beats you to it and welcomes Martin as Emperor Martin Septim. It would seem that your job is done except for one of those pesky messengers who always seem to show up and spoil things just when it looked like you've finished. Oblivion Gates have opened throughout the city and the city is being invaded by Daedra (including a couple who invade the Council Chamber). Martin says that he needs to get to the Temple of the One immediately to relight the Dragonfires.
As soon as you step out of the palace, you're going to be attacked by a veritable horde of levelled daedra. Like the Battle at Bruma, you'll need to keep Martin alive until you reach the Temple of the One in the Temple District. This isn't as hard as it seems since Martin knows he needs to stay alive to reach the Temple and you'll have help from Jaufre, Baurus/Steffan and whatever Imperial Guards are handy. Getting into the Temple is easy enough -- you just run for it. The problem is getting Martin to run behind you and keep him alive while you do it (remember, he stopped being essential about the time he gave his pep talk in the "Defense of Bruma" quest).
However, like you, he's interested in getting to the Temple of the One, not in fighting infintely spawning Daedra. And, on the bright side, Ocato is essential. It's good to have a swarm of Imperial Legion Guards (who are all 10 levels higher than you) and an unkillable level 32 Battlemage on your side. On the downside, though, he's a High Elf and tends to go unconscious a lot because of all of the spells being hurled around.
As you get near the doors to the Temple of the One, your next headache comes in: Mehrunes Dagon himself. Your journal tells you that lighting the Dragonfires will no longer keep Oblivion away and you should ask Martin what to do. A hasty discussion with Martin reveals that you should still get him to the Dragonfires. He won't tell you what he has planned, but an idea has come to him and he knows what he needs to do. But how to deal with Dagon, who is blocking your way.
You've already been given the answer. You can't kill Dagon, but you can certainly hurt him. If you have any nukes laying around (really heavy weapons or spells), now would be the time to get them out. A couple of really solid hits will stagger Dagon and let you and Martin get to the door. Once you're in the Temple, you only have one thing left to do: talk to Martin. He will run over to the side of the Temple and wait for you. Once you activate him, he tells you that he's sorry he won't be around to help rebuild Tamriel, thanks you for your friendship and says goodbye. At that point your controls lock and all you can do is watch the final action.
Martin runs to the center of the Dragonfires just as Dagon breaks through the roof of the Temple and steps in (good thing you're off to the side or you might have been squished). Martin smashes the Amulet of Kings, which releases huge gouts of flame that soon consume Martin and transform themselves into a great, fiery dragon. The dragon attacks Dagon (who gets in a couple of really good hits of his own) before Dagon is consumed by the flames and sent back to Oblivion. Obviously injured from the battle, the dragon spreads its wings, throws back its head and solidifies into a statue. Martin is nowhere to be found. Tamriel has lost another emperor.
Once your controls are unlocked Chancellor Ocato comes to talk to you. The Elder Council will have to make a decision about choosing another emperor, but sees very difficult times ahead as the provinces try to break away. I see the seeds of Elder Scrolls V.
Ocato has one additional topic: Champion of Cyrodiil. Ocato names you Champion of Cyrodiil, the highest rank in the Order of the Dragon, the knightly order founded by Tiber Septim. He orders a suit of Dragon Armor prepared for you which will be ready in two weeks. The Imperial Dragon Armor is a separate quest, but since it only has two stages that concern you, I'll deal with it here. With Ocato's announcement about the armor, a clock has begun ticking. In 14 days, you'll get a journal entry telling you that you can pick up your armor at the Imperial Legion compound in the Imperial City. At any time after that, you can pick up your armor and the Main Quest will be officially complete.
Congratulations, Champion of Cyrodiil. Tamriel has been saved, but the fate of the Empire is still undecided. Perhaps we'll see the resolution of that in the next Elder Scrolls.