Before the world ends...
The early turns of the game are spent ramping with Noble Hierarch, searching for combo pieces/miscellaneous creatures that fit the situation with Eladamri's Call, and possibly disrupting your opponent with whatever you happen to draw.
During these first turns, the best cards to play are:
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Aether Vial
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Noble Hierarch and/or Flagstones of Trokair and/or Ramunap Excavator
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Ghostly Prison and/or Windborn Muse
Once you have the combo in hand, it's simple: play Celestial Kirin, then cast Ugin's Conjurant!
One handy thing about this combo is that once you have the Kirin in play, your opponent is unable to stop it without a Stifle effect like Trickbind or Disallow; since Kirin's ability triggers on cast, whether or not Ugin's Conjurant actually resolves is negligible, and they can't play a removal spell on the Kirin before you cast it. That makes the combo completely uncounterable with an Aether Vial on 4!
You can pull off the combo as early as turn 3 with Noble Hierarch or on turn 5 for 0 mana with Aether Vial.
You have to pay your taxes!
The tax soft-lock is having Ghostly Prison or Windborn Muse on the battlefield and then Armageddon-ing (can also Vial in a Muse after combo). If they can't pay their taxes, they can't attack you!
Ghost Quarter + Leonin Arbiter + Ramunap Excavator is also a land lock after the combo, though they'll get one use out of most lands they play before you can do anything about it. (Note: The current version of this deck doesn't play Arbiter for various reasons. It's still a decent card to have, though.)
It's one of life's certainties.
After the end of the world, you will generally be left with a Celestial Kirin on the battlefield that you will then beat them down with in subsequent turns. However, there is a chance that your opponent will start to play lands and be able to stop you in the midst of that process, and that's when the next phase of the plan begins!
These cards fall into two categories: the ones that let you do stuff, and the ones that keep your opponent from doing stuff. I would make up code names for them but I suck at that so:
The Ones That Let You Do Stuff
Aether Vial, Noble Hierarch, Ramunap Excavator, and Flagstones of Trokair are the cards that keep you going post-Armageddon. Vial can handle the playing of larger creatures while Hierarch and Flagstones of Trokair give you some mana to cast the small things with.
Ramunap Excavator is the true MVP here; not only does it let you make land drops out of the ones you destroyed, but it also lets you loop Horizon Canopy and Ghost Quarter to draw cards or destroy lands every turn!
The Ones that Keep Your Opponent From Doing Stuff
This leads us into mana denial. Small Thalia, Big Thalia, and the aforementioned Ghost Quarter all deny your opponent the ability to pay their taxes, keeping them imprisoned forever!!!
(Note: Leonin Arbiter, Aven Mindcensor, Mana Tithe are also cards that work well in this deck.)
