Success in Teamfight Tactics means making the most of the resources you're given in order to combat the game's built-in RNG, requiring an intimate familiarity with all of its units and items in order to properly maximize the value of what you end up with in any given match. Here are some tried-and-true team comps and how to work up to them on the current 9.16 patch.
Draven
Pretty much the one thing that's remained consistent throughout Teamfight Tactics' lifespan is Draven being really, really good. Since he's a four-cost unit and won't have a chance of appearing until the mid-game, it's not possible to build around Draven every time, but you can lay a solid groundwork should he show up.
Fiora is an early Blademaster who can synergize with Draven later on, though she should be replaced by a stronger Blademaster later on should one appear. Team her up with an early-game Garen or Vayne and look to Knights, Nobles and/or Rangers to help you survive until Draven appears.
Equipping Draven with a Rapidfire Cannon and Bloodthirster is a must. After that, Phantom Dancer, Guardian Angel and Morellonomicon/Red Buff are some generally good items that can strengthen him as your carry. Draven comps generally utilize the Blademaster synergy, but if you're rolling lots of Imperials, the double damage from four Imperials is a pretty major buff to an already hyperstacked Draven.
Example comp: Draven, Yasuo, Aatrox, Gangplank, Shen, Camille, Swain, Katarina, Darius
Gunslingers
With the addition of Hextech units to patch 9.16 came Jinx, who is currently Draven's hypercarry counterpart, similarly capable of winning fights almost singlehandedly.
Gunslinger units appear frequently during the early game, since both Tristana and Graves are one-cost units. Look to start with a Gunslinger synergy, incorporating either Brawlers or Knights for some added tankiness in the early game, or a Gangplank if you luck out and find him early on.
Jinx similarly works great with a Rapidfire Cannon and Bloodthirster, though the latter can be subbed for a Hextech Gunblade. If the RNG gods deny you a Jinx, a hyperstacked Gangplank can also carry a Gunslinger comp. Guardian Angel is a must for Gangplank, since his barrels stay on the board after his death, and he will be revived with however much mana he had before dying. Morellonomicon/Red Buff are extra powerful on Gangplank, since their burn/anti-heal effects will apply to anyone hit in his barrels' large explosion radius.
Example comp: Jinx, Gangplank, Lucian, Graves, Miss Fortune, Tristana, Vi, Cho'Gath
Nobles
With the current patch, Nobles dominate, since the six Noble buff majorly increases survivability, which is useful pretty much across the board. The bad news for anyone hoping to build Nobles is that this comp relies on finding the five-cost Kayle. The good news is that the road to Nobles is fairly fluid and adaptable.
In a completed Noble comp, none of your Noble units are ideal hypercarries, so a Draven, Jinx or other good carry is a must. This means that your early game can be focused on Blademasters or Gunslingers, with a bench full of whatever Nobles happen to show up. If your early game team isn't cutting it and you feel the need to roll or level up just to survive, it's easy enough to count Nobles out and shift your focus onto a Draven-based comp, for example. If you're killing it early game, feel free to roll a few times for a Kayle later on in hopes of finishing the comp before any opponents hoping to do the same.
If you're denied a viable carry unit, you can pretty safely stack Vayne as a back-up. Vayne in particular is makes good use of Frozen Heart, with a high max HP at level three and an ability that deals true damage every three attacks.
Example comp: Kayle, Leona, Lucian, Garen, Vayne, Fiora, Draven, Camille, Jinx
Voids
Early game Void units Kassadin and Kha'Zix can have a huge impact given the right items (defensive items on Kassadin, offensive items on Kha'Zix, and attack speed items on either). With only four units needed to complete the Void synergy, they can be utilized in a couple of strong compositions.
Since the full Void lineup already includes two Brawlers, adding extra Brawlers is simple enough. Stack Cho'Gath, Volibear or Reksai with defensive items like Thornmail and Warmog's Armor for a meaty frontline, alongside other generally useful items like Guardian's Angel for survivability or Rapidfire Canon to prevent melee units from getting cut off from the action.
Alternatively, Sorcerers make good use of the Void synergy, since Kassadin contributes to the total number of Sorcerers, and as a whole, Voids add tankiness to an a team with otherwise low HP across the board. Look to stack Kassadin, Karthus, Ahri or Aurelion Sol with mana generating items like Spear of Shojin and Seraph's Embrace, ability power enhancing items like Rabadon's Deathcap, and the usual slate of staple items like Rapidfire Cannon.
Example comp: Cho'Gath, Rek'Sai, Kha'Zix, Kassadin, Karthus, Aurelion Sol, Ahri, Veigar, Morgana
Your Favorite Unit
If you have a favorite unit that you happen to find helps you win more often than not, or else just generally fits your preferred playstyle, absolutely build around them. It could even be possible to slot them into a slightly modified meta comp in certain scenarios. Plus, a well executed off-meta team comp with the proper items will always beat a poorly executed meta comp relying only on the right units. Since adaptability is key, learn to recognize early on if you're playing a Draven game, a Jinx game, or a game where you just really feel like making that level 2 Morgana work.