You and Me! (W): This is the ability that brings the rest of Yuumi's kit together. Targetting an ally with it will cause you to dash towards them if you're in range, and upon reaching them you will be attached to them and become untargetable but incapable of moving or attacking. While attached your Prowling Projectile and Zoomies will have altered effects but most importantly you and your anchor will receive AP/AD that scales with the anchor's pre-existing AP/AD. This is Yuumi's most intimidating feature as it can enhance a hypercarry's output greatly.
Flaws: This ability has a long cooldown after initial attach in early/mid game which is indicated by a bar above the ability icon. If you quickly detach to apply Feline Friendship be sure that it's fully recharged so that you can rapidly re-attach and avoid being open to CC. Note that while attached to an anchor however you can still dash to another ally without needing W's cooldown refreshed.

Zoomies (E): Yuumi's E is her trademark heal which also comes with an often overlooked movement and attack speed increase. If attached to an ally using You and Me! Yuumi will apply the effects of Zoomies to her ally instead. Most of the time you will only be using E while attached since Yuumi does a great job of avoiding damage by just staying attached to someone.
Flaws: Zoomies heals much but at a large cooldown and huge cost to Mana. For burst healing I reccomend you take Heal to supplement Zoomies in key moments.
The biggest flaw of Zoomies is that it costs a percentage amount of your maximum Mana, meaning you cannot effectively build mana granting items. You can however build mana regeneration, but in the end the best way to regain Mana for Zoomies is to effectively use your Feline Friendship.

Prowling Projectile (Q): Yuumi's Q fires a projectile towards the cursor. Its damage is not much at base but it's enough to validate AP Yuumi. What makes this projectile unique is not just the fact that it deals a percentage of the target's current health as damage but the fact that if Yuumi is attached when cast, then the projectile will home towards her cursor for the full duration granted she stays attached. This allows her to proc the empowered version of Q much more easily since it needs to travel for a full second before hitting a target to trigger the slow, bonus damage, as well as current health damage.
Flaws: Unless you count the cooldown for the third time the only flaw I can think of is that minions can easily block this projectile from hitting your intended target, and that many times you will be screwed over by U.I. or enemies being out of screen if you're on the top side of the map. This is where you'd try to practice using unlocked camera to hit more difficult shots. Do try not to waste your mana on trying to hit with this ability repeatedly because each attempt costs Mana, reducing the amount of healing you can do.

Bop 'n' Block (Passive): This passive single handedly gives Yuumi most of her combat-based skill expression. Without it she'd literally be unplayable so you best not forget about it as it will win many fights for you and your team. This ability, when refreshed, will generate a shield after successfully damaging an enemy with your auto attack as well as generate a percentage of your maximum Mana. You cannot be attached to proc this ability which can leave you vulnerable to damage and CC, so minimize the amount of time that you are unattached and make sure to go for bops when you're not in danger of being CC'd.

Final Chapter (R): Final Chapter is a very simple ultimate that launches many waves in a straight,unmovable line. If an enemy is hit by 3 of these waves they will become Rooted which leaves them open to attack. The cooldown for this ultimate may start pretty long but you'll find it to be very short in the mid-late phase of the game. The potential to root a full team of enemies is what makes this ultimate very powerful, especially when paired with the fact that you can perform the entire ult without once becoming targetable meaning you cannot be killed or interrupted for the full duration of the ultimate. When building First Strike your best damage output will come from activating it with Empowered Q and then Ulting on your target. First Strike will not only boost most of the damage you deal in that situation but it will generate a generous amount of Gold if you've managed to build a good amount of AP.