Shared Fate decks win by resolving Shared Fate onto a clean board. They have zero legitimate win conditions, so that once Shared Fate resolves the opponent is locked out from winning the game. The style of play is very controlling - with the entire plan being to keep the board clear of threats, use discard to scrub the opponents hand of enchantment removal, and land a Shared Fate for the win.
With Shared Fate in play, our opponent will be drawing out of our deck - so it's important that we don't include any ways to deal damage to players - or otherwise reduce our opponents life total. If we lock the board at 1 life, we want to be assured our opponents won't top-deck a Lightning Bolt and kill us with our own card. No win conditions means no plan B, which may be the biggest downside to this deck - if your Shared Fates all get exiled by a Surgical Extraction you may as well concede. However if you resolve Shared Fate and your opponent has no threats on board or in hand, they may as well concede. What could be more enjoyable than a game state where you know you have a 100% chance to win.
Cards choices
3x Shared Fate - The sole purpose and namesake of the deck. By resolving a Shared Fate you ensure that your opponent no longer has access to cards which enable them to win the game. Presumably our opponent will have win conditions in their deck. We of course have none in our own deck. So they can't win. They will still however have access to their cards in hand, as well as their board state, so care must be taken to keep these under control. Running three main and one additional in the board rather than four main because we don't want multiples in our opening hand, and we're comfortable waiting around to draw one.
3x Fiery Impulse - Normally you would see Lightning Bolts here, but we can't run them because they would give our opponent a way to finish us off after they start drawing out of our deck. Fiery Impulse is better than Galvanic Bombardment because it will more reliably be able to act as a Lightning Bolt against creatures. Galvanic Bombardment may warrant some testing, but only as a 4-of, which may or may not be what the deck wants to play (Terminate seems better than the fourth bolt).
2x Terminate - Catch all creature killer at instant speed.
1x Dreadbore - A nod to Nahiri decks. The Terminate/Dreadbore numbers should be meta-dependent. Instant speed is only valuable if you aren't about to lose to Emrakul.
4x Mana Leak - Leak is possibly at its best here. It's good at countering early threats to help us survive to cast Shared Fate. And once Shared Fate is in play, we should have enough lands that we don't have to worry too much about our opponent using it against us. Note that we can't run Remand because the opponent could use it to return threats back to their hand post Fate. We want to keep them locked out of their own cards!
2x Pyroclasm - Sweeps away all those silly little creatures.
2x Anger Of The Gods - Sweeps away all those slightly bigger creatures, FOREVER.
2x Damnation - Sweeps away ALL THE CREATURES! Seriously, we want to sweep the board early and often, and then still be able to sweep it later too. Shared Fate doesn't do anything to answer the board on its own, and it isn't hard to die to our opponent's board state because their deck ran less removal than you were hoping. Resolving a Shared Fate with a Damnation in hand is pure gravy.
4x Inquisition Of Kozilek - Targeted discard to strip early plays from our opponent's hand. Can also grab enchantment removal.
3x Thoughtseize - More targeted discard to help us throughout the game. Usually Thoughtseize and Inquisition are bad top-decks, however this is not the case here. It is important to use them to look at our opponents had and clear the way for Shared Fate. If the coast is clear it's a guaranteed win.
4x Serum Visions - The necessary evil when playing blue in modern. We need it to dig for Shared Fate, sweepers, land, whatever. Preordain this is not, but play it we will.
4x Ancestral Vision - Jeebers this card is amazing! Suspend it turn one to draw into Shared Fate. Suspend it before casting Shared Fate to resolve it into the opponent's deck. And best of all, our opponent can't even do anything with it as long as Shared Fate is in play. Suspend only works for cards in your hand. So it's just a dead draw. Not only does the deck your opponent is now drawing from have exactly zero win conditions, but it also has six cards that do literally nothing.
2x Wheel of Fate - This one's just broken. It works similar to Ancestral Vision in that it's a dead draw for them post Fate, but it's effect is much more game breaking. If you can resolve it with Shared Fate in play it will clear out the opponent's hand, guaranteeing that they will never play a win condition for the rest of the game.
Early Game - Do what it takes to survive. Kill every creature that comes into play. Manage your kill spells and sweepers carefully to manage your life total while accruing card advantage.
Mid Game - Grind out the opponent's hand and board-state in preparation to cast Shared Fate. Be patient waiting for the perfect moment, as tapping out for Shared Fate at a bad time can cost you the game. Make sure the way is clear using Thoughtseize or IoK. Also consider whether you can manage the opponents remaining threats before casting Shared Fate. Don't rely on drawing removal out of your opponent's deck. If your only out is Damnation then casting Shared Fate will surely loose you the game! The best scenario to set up is to resolve Shared Fate while Wheel of Fate is suspended with 1 time counter on it. This way your opponent will have only one turn with their hand before it gets discarded and replace with a new one from your deck.
Late Game - After Shared Fate is resolve you should play threats from your opponent's deck one at a time until the game is over. Remember, you're now playing against a deck filled kill spells and sweepers, and your opponent can't win so there's no rush. If a library should happen to run out of cards, no one will lose, because no one is actually "drawing" any cards. So if you're concerned about inevitability, just don't be the first one to run out of cards.