So to start the guide I should explain Yuumi is a cat and.. that's it, she's a cat.
She well.. purrr and things, and basically double the annoyance of any champion in urf, chase you down, help allies chasing, help them escape if something goes wrong, instakill you after she got 3-4 items, and she sit on a flying book.
So Yuumi from what I noticed so far is banned in like 2 of 10 games, because and that is just an assumption, because of her enchanting power, steorids on the literal meaning of word, giving up to 200% movement speed (maybe even more but I didnt get more until now Y_Y) and poking really, really hard from a safe spot (the ally champion). on URF she has basically a 3 seconds charge heal, which is extremly op, but you must have in count, healings early game are reduced a lot, so main abuse of this skill should be used for dodging skills (and i will stop right there with details because if i continue then I will have nothing to say in gameplay

There is a single good Yuumi build on urf and that one is completly chaotic ap one, you want a Rabadon's Deathcap first for it's huge AP stats and AP mutiply from passive, then you can just go for Spellbinder. You do not need any boots since you have a catapult to come anywhere on map, and once you arrive you will just attach on someone. There are some situational items you may take, but just in certain situations. For example will not be very meaningful on Hecarim or Veigar since they will kill all enemies before even auto attacking them, so Ardent Censer is a good item on champions that can use of it's passive, like Yasuo, Jinx or any other champion based on dps and not burst, mostly being adc.

Luden is a good rune for poking, and that .. that is all, take it, it's AP amount is good but you will trade some raw stats for a passive poke, mana and cdr don't really help you there so Luden is not as impactful as on normal Summoner Rift, still if you are the damage dealer take it, but honestly, most of time I recommand just going for another spellbinder

So maybe some of you asked the question, why taking 4-5 spellbinder instead of 4-5 Rabadon, I'm sure most of them didn't but I feel like I need to expalin, so, for once, Spellbinder cost 2900 gold, while Rabadon is 3600. Second, Spellbinder gives much better stats (ap is the same on both, but binder also give movement speed, not like you will use it anyway, but it's nice to have. Both Rabadon and Spellbinder have unique passive (and unique active on Spellbinder case), so taking 5 Rabadon will give you same amount of ap as taking a Rabadon and 4 Spellbinder, but you will also save a lot of money going for it.

Dark harvest, that's it, that's all you need to know.

Domination offers best offensive setups, while on sorcery you get .. mana, movement speed while using ult (spoiler most of time you ult while attached), absolute focus and gathering strom is nice tho, so I will say it's more a preference than most optiomal setup, but again, I think Dark Harvest works the best. Taking it will also give you a free execute on Q after you stack some ap and DH.
Well you will play Yuumi pretty much like a normal Yuumi, except the fact that you spam Zoomies every 3 seconds and constatly snipe enemies with Q. Be sure to take as many harvest as possible tho, as the game is going on you may be surprinsed to see how much damage you can do, but most important things will remain in Zoomies that being the movement speed which I alerdy mentiong early in guide, it's huge with enough ap.
Also you may noticed I didn't put in the guide a order with what skills to max, that because, is kind of situational, for ex, you may start with Q if your ally have no poking skill, or start with E to sustain him until level 2, usually you max either E or Q and then put 2-3 points in You and Me!, then max the other skills (Max W last, unless you feel like maxing Q last, but you want Zoomies always being max first or second).

If you are interested in more Yuumi, there is a guide (kinda outdated, I will updated when I have enough time, most of things are still viable tho) for Yuumi, it explains better how skills works and gameplay in general https://www.mobafire.com/league-of-legends/build/yuumi-guuide-9-14-551196