Yuumi is weak early. She's not as squishy as she looks (thanks to the passive and her E), and she hits harder than you'd expect (E's AS; and Yuumi starts at a respectable 55 base damage). However, her only early offensive button is Q so she can't really stand toe to toe well. Yuumi wants to aggressively short trade; pop pop pop with Hail of Blades, back off if they don't run, repeat as often as they let you and don't be gun-shy about it.

The fastest way to get Yuumi doing real damage is to go for Blade of the Ruined King and then more AS afterward. Keep in mind that BotRK is best to buy early, before enemies can start stacking armor -- it is an excellent first buy on pretty much any champion that doesn't spam offensive spells, even a Yuumi.

Berserker's Greaves + Runaan's Hurricane ramp your early game quickly while setting you up to be reasonably dangerous in late game. You want to prioritize getting more AS as much as you can. The only reason to get other items is to keep from being burst down, since attacking faster gets you health back from BotRK's lifesteal. Possibly you can go into Spirit Visage to ramp the healing that way, if you are against a champion that does mostly magic damage and/or you want to ramp your E and Heal a bit (when used on yourself).

All other items are to help you survive so that you can farm. Build some basic armor or MR if you are getting dove or ganked. Buy Sapphire Crystal (and maybe some armor/MR with it) if you need to use E liberally to stay in lane. Cheaper CDR items are helpful if you need to spam E often or team fighting starts early (to have R up more often). If you need to push into towers, Frozen Heart is extremely good for that. If you need to help contest lots of objectives, Wit's End (for extra AS) or some CDR (for R) is good for that.

Going into a defensive item right after BotRK can be OK if you just want to win poking trades vs a champion that doesn't heal inside combat. For example, you can go BotRK + Frozen Heart vs someone like Garen and then poke him to deny farm. Building AS (mainly Berserker's Greaves to stay away from Garen) and some minimal armor can be much more effective though, especially if the enemy jungler and midlaner do any magic damage (because they easily roam up to you).

There are those games, and you must recognize them, where you will contribute more with your R than with any of your healing or damage. In those games, get your CDR right after BotRK. Frozen Heart + Kindle Gem (maybe into Spirit Visage, maybe into more AS to draw aggro to you) will make you a pretty reasonable engage tank to front-line for your team. You can tank autoattacks and towers pretty well -- and the enemy will not expect a Yuumi to be able to do it, even after they look at your items. If the enemy are dumb enough to target you, make them sad by jumping onto a teammate once hurt and then jump off again once E is back up to heal yourself. If they ignore you, BotRK will do work and you have heal/cc for your team.

I built this because Yuumi's damage on her Q is beyond awful. This means if you want to do more than heal people and hit R once in a while, you have to go into something like Nashtor's Tooth + Lichbane (which does work). But I wasn't satisfied with that level of damage, and it left Yuumi squishy to where she couldn't be unattached to fight. So I made a tank Yuumi that can do some damage. Enjoy.

As with top lane, expect your damage contribution to be virtually zero unless you rush BotRK. However, I do find that getting health, armor, and/or MR on first back can be helpful to staying alive while trying to poke at two enemies at once. These items help you use E without sidelining into AP buys. Taking less damage means E on yourself is stronger, and it also lets you poke more safely to proc your passive and get some mana back. Raising your max health makes it easier vs a mixed physical/magic enemy duo, to get in there and proc your passive.

I have found myself going BotRK + Berserker's Greaves, then going into my CDR items to get more access to R. Your ultimate is a big part of what helps your ADC get kills, and it's also your best defense to help you and/or your ADC escape a bad situation. The Frozen Heart buy doubles as a way to help your ADC trade well vs the enemy ADC, since you are lowering enemy AS by 15%. It also lets you tank a tower for your ADC (or the jungler) if you dive a hurt enemy.

Melee champions with no engage, like Darius, can sometimes be ignored when looking at a team composition. Even if you are against Darius in the top lane, just BotRK and a ton of AS can ruin his day. Yuumi is a fast little cat, and once you add Frozen Mallet on top of it he's helpless.

Magic champions with limited burst potential, like Ryze or Evelyn, can sometimes be ignored when looking at the enemy team composition. Just having a bunch of health plus your constant lifesteal can be enough to shut them down as a serious threat to you. You can sometimes also make due with just one MR item instead of both. Frozen Mallet makes this sort of enemy miserable. They count on styling on you then backing out of the exchange; getting slowed wrecks them.

It is always worth TRYING to fit Frozen Mallet into the build as a late game item. You will have Runaan's Hurricane by then, so you can turtle power the enemy team. It helps you draw aggro to yourself, which is what the build is supposed to do. You take the damage then don't die, since you can just heal then jump to a friendly champion until E's cooldown is up again (or worse; hop back off immediately and use turbo-autos to lifesteal off of three targets while shredding people).

When games go stupidly long, you can opt to start transitioning back into an AP Yuumi if you want. Keep your CDR items. Transcendence will turn them into AP. I suggest trading out BotRK and Runnan's Hurricane for Nashtor's Tooth and Lichbane, then getting Rabadon's Deathcap in place of Wit's End. These AP items become strong in the ultra-late game because of Gathering Storm, which scales better with AP than with AD. You will have 40% CDR, a ton of AP, and all ranks in Q once you reach late game -- this is the first moment where Lichbane and Nashtor's Tooth start to do real work as damage dealers. This AS>AP transition can mess the enemy team's itemization up, as if Yuumi going AD didn't do that before. You are suddenly a major source of magic damage, where before you were almost entirely physical damage (autos + BotRK).

You can buy Guinsoo's Rageblade instead of Runaan's Hurricane when the enemy team does not group. This takes you from a constant 2.3 AS (2.4 if you take the 10% AS offensive perk over the 9 adaptive damage)to 2.15 AS ramping into 2.5 AS (pretty much always 2.5 AS since HoB is in effect for the first 3 shots). You get extra procs of BotRK and Wit's End, some damage from Rageblade itself (25 AD + 15 bonus), 15% pen on everything you do, and a marginal amount of AP (25) that you won't notice you have. You do give up how fast you can clear a minion wave or monster camp, but at 2.5 AS it's not a big deal. The real thing you are giving up is the 40% AD + on-hit effects that Runaan's Hurricane is spreading across the enemy team if they group up.

A few quick notes about Yuumi's 15% maximum mana cost on her E.

-- Her mana curve for E is about the same as the old one until you hit level 12. After that it begins to creep up past old costs, ending at minimally 105 more per E than before (165 more w/ Frozen Heart). Yuumi's passive ramps with the cost though, as long as you use it actively; your cooldown gets lower and your mana reward gets bigger, as you level. This is why tank Yuumi kind of works. She can walk in more safely to use her passive, relative to other builds.

-- Q and R don't have a percentage mana cost, so mana is still good there. E has a flat mana cost of 60 that does still reward mana buys even for E. Mana buys aren't bad on Yuumi now, just not as good as before. In fact the main change is probably that AP Yuumi will now always want Archangel's Staff (over Luden's Echo or Hextech GLP), in order to get its 25% mana use refund.

-- Get blue buff. Hunt down the enemy carrying blue buff. Pair with junglers that won't need blue buff after level 11 or so, which is when you'll start needing it. Honestly I'd say the best team for Yuumi would have multiple champions that have not much use for blue buff. Something like Renekton jungle and Vladimir mid leaves the bottom side blue free for Yuumi to go get, and if you are playing from top side (as support) that blue is free for Yuumi as well with an adc to help you get it quickly.

-- Don't heal squishy champions unless they have cc, if you are struggling with mana. Heal yourself and continue to off-tank, or heal another durable champion (like Renekton) that has dps and cc. Yuumi isn't really ideal to attach onto someone building no defensive items, even if you go AP Yuumi. You want them to tank up with armor/MR to make your healing more valuable, and you provide the damage by attaching. This is why I really hate seeing things like Ezreal + Yuumi. He's squishy af and can't back Yuumi up with cc when she goes in to proc her passive.

-- Try to pair Yuumi with a champion that has better cc than a root/slow. You want your adc to have a knock (Vayne's Condemn), stun (Ashe ult threat), or fear (Crittlesticks) to help guard you when you go in to auto-attack (especially if you go AP but it still applies here until you are built up).