This combo is the most elaborate thing I've ever seen in Magic, involving over 20 cards.
To start the combo, you need to ramp up a bunch of mana and cast Genesis Wave. There are two different infinite mana combos in the deck, the primary one being Metalworker and Voltaic Construct, but the Construct can also work with Mycosynth Lattice and Priest of Titania. When you activate the combo, make sure to play Staff of Domination when you can.
Next, use a second Genesis Wave, which should put your whole deck onto the battlefield, then the Elixir of Immortality will shuffle all the nonpermanent cards into your deck, which you can then draw with Staff of Domination and your infinite mana. At this point, every permanent in your deck should be on the battlefield, and the rest in your hand.
Next, cast the Research half of Research // Development to grab a few cards from your sideboard and put them into the deck. You won't have to worry about mana colors because of Mycosynth Lattice. Use the Elixir of Immortality again to shuffle everything back in, then draw them all with Staff of Domination. Repeat this process until all the cards from your sideboard are in your hand.
First, cast Hive Mind, and then Channel the Suns to add one mana of every color to both player's mana pools. Shuffle it back in with Elixir of Immortality again, then redraw it again with Staff of Domination. Repeat this process until both players have a monstrous amount of mana of every color in their mana pools. From there, cast Vedalken Orrery, Mirror of Fate, Cast Through Time, and Door to Nothingness. This is where stuff starts to get nuts.
This next portion is entirely dependent on the order of play. Use Staff of Domination's card draw ability to put it on the stack 7 times, but don't let it resolve. Sacrifice Mirror of Fate, and put it's ability on the stack too. Mirror of Fate doesn't target, so don't worry about that part yet. Next, cast Paradigm Shift. Hive mind makes a copy of it for your opponent. Cast Through Time gives it rebound, so it'll be exiled instead of put into the graveyard. Don't worry about choosing to cast it again next upkeep. Sacrifice Elf Replica, target Hive Mind, then let only that ability resolve. Then cast Decree of Annihilation, which will also get Rebound just so you can exile it.
Next, with everything still on the stack, cast Oblivion Ring and let it resolve, targeting Door to Nothingness. Cast another Oblivion Ring to exile Vedalken Orrery. Now let the stack resolve. It should look like this:
Decree of Annihilation
Paradigm Shift (opponent's copy)
Mirror of Fate's ability
7 instances of "draw a card"
Decree of Annihilation resolves first, exiling all cards from all graveyards and all hands, and because of Mycosynth Lattice, all permanents of all types. When it rebounds, it is also exiled, leaving your graveyard empty. Vedalken Orrery and Door to Nothingness come out of exile from their Oblivion Rings. Next, Paradigm Shift resolves for both players, exiling both libraries and leaving no cards anywhere other than exile.
Now, Mirror of Fate resolves. Retrieve these 7 cards:
Upwelling
Omen Machine
Lich's Mirror
Donate
Twiddle
Oblivion Ring x2
The last thing left on the stack is Staff of Domination's "draw seven cards" ability. Let it resolve, putting the 7 cards you just retrieved into your hand. Cast each of those cards except the two Oblivion Rings. Use Donate to give your opponent Door to Nothingness, then untap it with Twiddle. Remember that both players have a huge amount of mana from Channel the Suns, because the phase hasn't ended yet.
Your opponent now has three choices: Activate Door to Nothingness targeting themself, activate Door to Nothingness targeting you, or do nothing. The goal is to get your opponent to use Door to Nothingness on themself, but it won't always be easy.
If your opponent targets you with the Door, cast the Oblivion Rings with the Door's ability on the stack, exiling Omen Machine and Vedalken Orrery. Then the Door's ability resolves, and Lich's Mirror shuffles everything into your library, at which point you draw all 7 cards back. Then the Oblivion Rings will resolve, returning Omen Machine and Vedalken Orrery to the battlefield. Because of the Orrery, you can cast everything at instant speed, essentially resetting the board and giving your opponent the opportunity to make the right decision.
If your opponent refuses to use the Door on themself, you may need to force them. To do this, use Oblivion Ring to exile Omen Machine during their upkeep. Even if your opponent tries to respond by using the Door on you, Lich's Mirror will keep you from dying and will get rid of Omen Machine, which lets your opponent draw a card and lose the game.
If you're not about giving your opponent choices, you can replace Lich's Mirror or Omen Machine with Mindslaver for force your opponent to die. The cool thing about this combo is that there are so many cards that could be substituted for others and still make the combo work, but in various different ways. For example, you can use Hive Mind and Paradigm Shift along with something to exile the graveyard to make your opponent lose over and over again. You can also include Shahrazad to start a subgame where they draw and lose, then use Elixir of Immortality to regain it and cast it again and again until your opponent is dead, but with this one, you have to make sure you have 7 cards in your library when you reset.
For a longer, more torturous death, you can use Oblivion Ring and Decree of Annihilation to exile all permanents, leaving you with Omen Machine and a method of destruction. Kobolds of Kher Keep and Orcish Oriflamme is fun, but you could use any single creature, such as... Storm Birds?
There's also the option of a ridiculously overkill death. You can cast Soul Foundry and use Karn's Touch to turn it into a creature. You can then use Voltaic Construct to give you an unlimited number of any creature in the game. Alternately, you could use a Jackal Pup, Donate it to your opponent, then use Soul Foundry to make a bajillion copies of Blazing Effigy. Then, kill one of them any way you want, then use the Blazing Effigies one by one to cause a chain reaction of damage to the Jackal Pup, and consequently, the opponent.
For a simpler overkill route, you could use Soul Foundry and Mirror Gallery to make a million copies of Progenitus, then give them haste with something like Hammer of Purphoros.
You could also replace Soul Foundry with Prototype Portal to create as many of any artifact in the game as you want. You can then imprint Booby Trap and make enough copies to name every card in the game a million times, then wait for your opponent to draw anything other than a basic land and watch the magic happen.
Another variation is to use Prototype Portal's imprint on Sculpting Steel, which will allow you to copy any permanent on the battlefield because of Mycosynth Lattice. You could make hundreds of copies of Standstill, then cast a spell to make your opponent draw more than their entire library. You could also make a thousand copies of Pyromancer's Swath or Pyromancer's Gauntlet to let you Zap for massive damage. And finally, you could copy a Planeswalker and get rid of the old copy and activate their abilities as many times as you want, such as Jace Beleren to mill your opponent or Chandra to win with damage.