DEMACIA
Is going to win through proper uses of ultimates in the fight. Jarvan's ultimate synergizes incredibly well with Vayne's E, allowing ehr to quickly dispatch a foe on the enemy team. Sona's ultimate synergizes extremely well with Lux's since chances are the champions Sona hits with her R will be in a line, allowing for Lux to dispatch them very quickly. If there's anyone on the enemy team that can stop all this due to them getting ahead earlier in the game, chances are they are the Villain, so Garen can quickly dispatch them and protect his allies.
Win Condition: Pure synergy and team work
NOXUS
It all comes down to the fight starts. If Sion or maybe even Morgana can get a good ultimate off, the rest of the team can swoop in quickly and snowball the fight off of just a single kill. It's a very simple win condition, but quick, snowbally death is really good one as well.
Win Condition: Snowball a fight off of a single kill due to your immense rewards for doing so
IONIA
Teamwork is essential here, which is shown off by the amount of benefits that the team can share with their carries, being Xayah and Syndra. Syndra can quickly dispatch one target while Xayah can deal some major AoE damage. The rest of the team is focused on making sure nothing happens to them in the mean time through shields, dodges, and crowd control. Daisy can even act as a meat shield for skill shots (sorry Daisy).
Win Condition: Win the game through pure team work and coordination, allowing your carries to be untouchable
PILTOVER
They can really rush a win if they can just get a few kills early on, which can be enabled through Vi's R ganks. If Ziggs gets a kill, he can quickly kill his tower. If Caitlyn gets a kill, she can quickly become a menace due to incredibly large critical strikes. If Camille gets a kill, the enemy back line will never be safe and her lane is as good as won. It's all about ending the game as quickly as possible.
Win Condition: Snowball the game into an early win
ZAUN
This is a basic war of attrition and Zaun is stupidly good at that. Through shields, steroids, and various other mechanics, Zaun champions can be a pain in the butt to kill. There isn't one big "this is the strategy, carry it out" or "it all depends on this one moment" kind of deal. Zaun is going to not care about what the enemy team does. Zaun does as it wants and does it well. They'll kill the enemy team or split push with Singed to force the enemy to make tough decisions. Zaun's goal is just to win fights and win the game. They just overpower their opponents through sheer force. That may sound bad on paper, but the enemy can't carry out their strategy if they can't win any fights either.
Win Condition: Kill them far more than they can kill you
BILGEWATER
Set up fights with crowd control and then dominate foes with stupidly powerful wombo combos. Even if they aren't able to pull it off, you'll be hard pressed to punish them due to their many defensive mechanics and slippery nature. Bilgewater is incredibly hard to fight since they have the potential to just do so much in a fight with the right moves. Plus, even outside of team fights, they can stop a split push very easily due to their abundant wave clear and GP's ultimate. The best way to win here is to out maneuver them and take as many objectives as possible to give your team the edge.
Win Condition: Achieve the wombo combo
FRELJORD
They're going in and they're not going to die. You'll be hard pressed to burst them down as well due to their many defensive steroids and plentiful crowd control. Similar to Zaun, but different in the approach. They are going to win because they won't die. They are hardy people and will make you feel like you are playing a standing still simulator with their crowd control and slows.
Win Condition: Disable the enemy team and then overpower them with your defensive mechanics
SHURIMA
Secure the early game with your extreme power houses of Renekton and Sivir while making sure your carries scale into the late game and become very powerful, namely Azir. Zilean provides tons of protection and Skarner can make sure they get the kills to scale. It's actually the most basic strategy that has been alive since the beginning of League. Shurima will feel very familiar strategy wise to play.
Win Condition: Crush the enemy early game so your carries are always one step ahead of them
THE VOID
Just get to the late game. The enemy team cannot win the late game, it's essentially impossible. It's very fitting since the enemy team feels like they have a timer above their heads, knowing that the impending doom of the Void is descending upon them. With the combined scaling power of Cho'Gath, Kog'Maw, Kha'Zix, and Vel'Koz, the enemy team simply won't be able to win late game without some near impossible plays. Cho'Gath will eventually become a near unkillable beast that will dominate the enemy team. Kog'Maw's been known for his absurd late game and his mixed damage makes him almost impossible to build against. Kha'Zix gains more and more evolutions over the course of the game, empowering his abilities and making sure the enemy never splits up. Vel'Koz eventually overpowers the enemy with tentacles tons of true damage that will make them be forced to build health, much to Kog'Maw's pleasure. Meanwhile, Malzahar makes sure they all can get to this point by securing kills and protecting them with his various means of crowd control and protection.
Win Condition: Reach the late game
SHADOW ISLES
Slow, yet calculated will be what describes this team. The enemy team WILL eventually wear down and they WILL eventually fall to your unending assault. Their ability to capitalize on mistakes and quickly decimate an enemy team by using their ultimates correctly will make the Shadow Isles a true menace to fight. They are, ironically, similar to Demacia in this way. They will be winning the game through good coordination and teamwork. I guess friendship is magic...ally painful.
Win Condition: Gradually weather your opponent's objectives and use coordination to chain together incredibly disruptive ultimates
BANDLE CITY
Very tactical team that will be winning by taking full advantage of what their kits bring to the table. While they lack durability, Lulu can more than up for that for one particular ally on her team when needed through her shields, crowd control, and ultimate. Veigar and Rumble combined make a truly frightening combo in a teamfight through Veigar's E and Rumble's R, creating large areas of the fight where enemies just can't stand in or combing the abilities together to obliterate someone. Speaking of which, Veigar and Tristana will scale extremely well into the game due to Veigar's infinite AP and Tristana's nature of chaining kills together. All of this is supported by Teemo, can also make his team artificially more durable by shutting down the opponent's ADC with his blind. Plus, Teemo's mushrooms reduce the enemy's own tankiness, making it so a good Teemo can lower the opponent's health pool down to a squishy's before the fight even starts.
Win Condition: Feed Veigar and Tristana and artificially increase your team's durability
MOUNT TARGON
You only got a few team compositions (in the single digits), so the enemy will know almost exactly what you are going to bring to the table every time. However, this doesn't matter if you can endure. All of the characters present are provide extremely powerful mechanics and, most importantly, can dive the enemy extremely well. If you can always crush the enemy's back line, it will leave their front line with less options for damage and allow you to secure a win very quickly since half the enemy's team doesn't exist.
Win Condition: Delete the enemy's back line from the game
RUNETERRA
You just gotta initiate so hard that the enemy team has no idea what hit them. You have so much crowd control and so much AoE damage and so much sustained damage that if the enemy team doesn't approach the fight correctly, they will die without being able to do too much about it. Even if you mess up, you have Kindred's ultimate as a back-up plan to make sure punishment is as minimal as possible. Basically, you are going to win the game by making sure the enemy isn't playing the game.
Win Condition: Disable the enemy team and kill them quick enough that they can't fire back much if at all