This is more of my main Yuumi build than a full-on guide, but I'll add a few notes here concerning itemization order. You build differently based on what you will need. Eventually you do it all.

Let's say you choose Yuumi, and you get stuck with yet ANOTHER Ezreal who thinks a Yuumi in his lane means he can't die no matter how badly he positions. Don't go for your CDR + AP items and play into his bad thinking. Build BotRK, Berserker's Greaves, and then go for your CDR + AP. You will be carrying the lane, because Ezreal will be getting himself killed and you'll have to guard the tower while he's gone. BotRK is low key really good for that, since you get enemies low very fast to where tower shots mean something. Full boots are also good, because 1v2 is hard.

Let's say instead, you are a farm lane. You are against Zyra + Morgana, and you are supporting an Ashe or something. No amount of kungfu is going to give your Ashe a ton of kills unless the opponents get caught by ults. Your job becomes keeping Ashe alive when she gets caught by something. Here you can go straight for your CDR + AP items and be priestess cat in the early game.

It can be good in some fights to go for Frozen Mallet + Berserker's Greaves first. Let's say you are trying to help Ziggs against an enemy lane of Sivir + Zilean. Both of those champions play WAAAAY back, so Ziggs struggles to do more than throw a lazy Q their way unless you can slow them down. Ziggs will get their tower early, and you'll be well built to chase opponents down the lane once he does.

I usually find the best item order to be BotRK + Berserker's Greaves, into Frozen Mallet + Forbidden Idol, into Nashtor's Tooth + completed Ardent Censer. I only pick up the Runaan's Hurricane in the late game unless we are struggling to win team fights or I end up split pushing (which this build can do once you have Frozen Mallet since you are fast, reasonably durable, and can just outfight half the champions that would normally come to 1v1 you).

I have in some games gone for Wit's End over Runaan's Hurricane to survive better vs something like Zyra. It's barely worth mentioning, as RH is just better overall to make the build threatening to the entire enemy team instead of just one enemy.

A special note on Gathering Storm manipulation here also; you can flip whether you are getting AD or AP with this build pretty easily. BotRK first gives you AD, but then if you need healing you can grab Nashtor's or Censer and now you have AP instead. It's pretty easy to switch back after that by going into Frozen Mallet... you get the idea. Fully built you are relying on your 2.4 AS, Hail of Blades, and BotRK for the bulk of your dps. Gathering Storm will be giving you bonus AP to ramp your passive shield, Q, E healing, and ult damage.

You will exceed 415 run speed with this build while slowing up to three targets by 20% (about -73 move, minimally). This means an enemy team that gets into your range must use dashes to get away or must turn and fight. Be ready for both possibilities. If the entire enemy team dashes away, you can aggro-Flash to catch them. If the enemy team turns to fight, have W ready to hop onto a teammate coming in behind you. This is how late game Red Dot Yuumi operates. You force fights anywhere you find enemies, or you peel for your entire team if things go south even when your ult isn't up. Yuumi is good at getting out as long as she can jump with W, and your E is cheaper if you are underleveled. Be the last to leave the fight.