Twitch and Yuumi are all about catching enemies off guard and instantly wiping them off the map; let's break down this stealthy bot lane duo.
Twitch is a versatile bot laner as he can build an AP or AD damage profile. AP Twitch focuses on his passive, generating a lot of stacks and letting the damage over time shred through healthbars. The slow from his W scales with AP, giving Twitch the chance to accumulate more stacks from his basic attacks and the W itself.
Meanwhile, most of the damage from AD Twitch will come from his basic attacks and E after some stacks have been generated. Both AD and AP Twitch can catch enemies off guard by popping out of stealth and getting off some surprise basic attacks.
Even though Yuumi is pretty vulnerable, she can afford to play a little aggressive in the early laning phase; she can basic attack the enemy, then heal herself to come out of the trade favourably. This can only be done if the enemy's hard CC is on cooldown, otherwise Yuumi is at risk.
Given how mana hungry Yuumi is, it's important to proc her passive as much as possible whenever it's safe to do so. The shield is permanent until broken and can be stronger than her E, as it's unaffected by Grievous Wounds and scales with Yuumi's level.
The main reason why this is such an excellent duo is because of their ultimate combo. If Twitch has popped his Q while Yuumi is attached, Yuumi will also be stealthed. This means Yuumi can catch people off guard and start to root them with her ultimate. Once they've been rooted, Twitch can pop his ultimate to start bursting down the enemy, and use his E to finish them off once some stacks have been generated.
Even though Twitch has some escape tools with his Q, he doesn't have any mobility and is susceptible to dives. Therefore, Yuumi can help protect him using her heals, shields, and ultimate if any enemy gets too close.
Additionally, Yuumi's W grants an adaptive bonus to whoever she is attached, based on the stats of her ally. She also gains this bonus for herself. This creates a snowballing effect as Yuumi and Twitch can continue to increase each other's stats the more fed they get. The adapative bonus can be AD or AP, meaning both Twitch builds benefit from this bonus.
AD Twitch is focused on attack speed, allowing him to generate more passive stacks quickly and get more basic attacks off during his ultimate. This can be done with runes like Lethal Tempo and Legend: Alacrity, and items like Blade of the Ruined King and Kraken Slayer.
AP Twitch still wants to build attack speed for quicker passive stacks, but will build items like Nashor's Tooth and Rabadon's Deathcap instead. Hail of Blades is a great keystone to generate a lot of stacks quickly, while Legend: Alacrity can still be taken as a secondary rune.
Summon Aery is a fantastic keystone on Yuumi: it increases her poke damage, procs Moonstone Renewer when she uses a W on an ally, and increases her shields. Yuumi is extremely mana hungry, so runes like Manaflow Band and Presence of Mind are essential for mana regen.
Yuumi will build standard enchanter items, like Moonstone Renewer and Redemption. She can also build Chemtech Putrifier against a lot of healing, and Ardent Censer/Staff of Flowing Water depending on your team composition. Given how much time Yuumi spends attached to allys, she doesn't need to buy boots so can rush other items quicker.
Twitch and Yuumi are one of the best bot lane pairs in the current meta, thanks to their ability to pick enemies off by comboing their ultimates while Twitch is stealthed. Their laning phase isn't the strongest, but they become much stronger in the mid to late game.