Started Playing Zilean: October 29th, 2015 (4/1/7), W
Record as Zilean in 2018: 47-21 (69.12% WR)
Current Win Streak: One
Total Mastery Points Score: 289915
(October 12th 2018)

Sorcery

Summon Aery: As a support, with the obvious exception of his ult, Zilean doesn't do much for his laner, and in the early game, if he doesn't hit his stun, he's pretty helpless to his ADC. Summon Aery is primarily taken for his E, as it not only speeds up his lane partner to get them out of a situation, or into an engagement, it provides them a shield as well, which in both instances can be just as protective as his ult.

Manaflow Band- Zilean isn't getting anyone with his AA game. He needs low CDR, so he can spam his E and his Q as much as they are available. To do that, you need mana. Manaflow Band, with Ancient Coin Build, helps keep your mana sustained early on, and later in the game keeps you topped up for long lengthy team fights.

Transcendence- The CDR by it's self is incredibly helpful and makes this I believe the most important rune of the build. It gives it to you early enough where it really makes a difference, either just finishing up laning phase, or starting to team fight a bit more. Going from most likely 15% to 25% for free makes Zilean so much more potent. The excess CDR converting to AP later in the game is a bonus. If you get into the late late game of one of those long matches, you will find a lot of the situational items come with CDR, which you've been at 45% since 25 minutes

Gathering Storm-This is the only rune I ever consider switching, for Scorch. Scorch is the much more useful one, providing some burn damage on your Q's early game, every ten seconds, which is about what Zilean's Q starts at early game. If you know youre in a matchup where you need to win early and fast, switch to Scorch.
The reason I take Gathering Storm, is I'm greedy. And preparing for a late game.Once Zilean is about level 4, aka has 2 points in his Q, and has minimal AP, his bombs can start to really hurt. Like a surprising amount. So I find I don't really need that extra scorch damage early game. I don't usually find myself wanting to engage pre-level 4, using my bombs just to get scorch ticks instead of having them in a fight for a stun. Once Zilean then has his ult, some mana regen, and a smidgen of CDR, he can really put on some pressure on his own. So I take gathering storm to help Zilean stay relevant if a game goes late, where that surprising Q damage tends to not be as impressive. And if it only goes to the 20-30 minute mark, there is stil around 24-48 bonus AP, which again, for free is a really handy boost to keep the Q damage helpful, and to make the Ult healing a bit juicier.

Inspiration
Biscuit Delivery- Before your items are coming in and before manaflow band has stacked, biscuits are a super helpful way to sustain in your lane. You save money on potions, you get mana regen and more mana, and you get some healing, which when you are running oom, popping a quick biscuit can give you enough pep for a quick speedburst out of a tough fight.

Cosmic Insight- More CDR. The more the better. Plus this allows you to max your CDR cap at 45%, which come latest of games can give you access to permanent slow or speedup, ridiculously quick timers on stun capability, and the ability to ult less than every 30 seconds. in a long teamfight, that can provide a bunch of extra burn.

This section will just cover the why on my questionable and very not support looking item choices
Lost Chapter-
What an Item. Can I first give a shout out to Old Morellonomicon? Man that item had everything. Mana, Mana regen, loads of AP, tons of CDR, Grievous wounds effect. It was beautiful. Now new one is still an item we want, but it's build components don't give us the mana sustain we crave as Zilean. So we build Lost Chapter, that will get used, but not right away.
Heads Up. I'm going to throw MR boots on the main build, but the boots can be very situational. Usually I'm between the two defensive ones, MR and Armour. In some situations, especially if ahead, it's definitely a play to go for the quickness boots.

The Main Frame-
This is the magic key to success.
I go through phases of finishing either of the AP items first. Benefits for both:
Morello's. Grievous wounds is so helpful for those early and mid game team fights, preventing them from healing as much, as well as the little extra bite of magic pen, and a bit more health. Extra health can keep you alive that much longer to save a teammate, and send out some more damage.
Ludens: Gives you a whopping amount of mana. And a lot of CDR. Completing this item maxes out your CDR. So if you wan't the CDR right away, and a little bit of splash damage with your Q, Luden's is spectacular.

The Situationals-
Wow, you're probably saying, this sure looks like it's pretty much a Mid Zilean build, other than that single support item. You're right. But I don't find Zilean to be as helpful, running the classic support items. A reminder now that my matches skill levels should be falling in the 'played 3 ranked games in my life' area.
Zilean with some tankiness and some AP, and a lot of mana and CDR, can supply tons of CC, damage and some very nice heals via his ultimate.
Out of these situationals, I will usually build the Banshee's and the Zhonya's. The excess CDR helps boost your AP, and the effects of both the items help give Zilean more tools to stay alive, so he doesn't have to waste his ult on himself.
In a game where a team is all AD, and in rarer cases all AP, or if very far ahead, I will pick up Liandry's instead of one of these items, or if it's that late, boots.
I threw abyssal mask on here. Not going to lie, not sure I've ever built it. But I wanted a real defensive option if that was ever something that you needed to stay alive, as well as an aura passive I just read and honestly might try next game, because it looks really strong.

Max Ult as soon as you can. Max Q as soon as you can.
My usually pattern is putting a second point into E just before maxing out the W. I prefer maxing W first, because again, my main goal with Zilean, is max CDR, being able to cast as many spells as I can. I find when I don't max W first, sometimes there will be team fights where I go to throw my second Q>W>Q, and W isn't there yet. Without W, Zilean has very little to add in terms of effectiveness in a team fight. And a 55% slow for 2.5 seconds? That's all you should really need until all your other abilities are maxed.

Here's a big play that can potentially help you max out the effectiveness of your passive.
Level 1 going level 2, you see that juicy yellow circle light up and you just want to click them. Don't. It's not worth it. When you see that yellow circle level 1, they are 1 creep away from getting level 2, they don't need your handouts. Save it for level 3, because when that circle turns yellow, you have more xp in you to give, and they are a few minions away instead of one. Past that point, give it to your ADC whenever possible after that, or look for players in the mid game who are approaching big levels, such as 11 or 16, to help them get their ults better faster.

Alright. Here's a couple Brules rules for your health, and more importantly, what you need to control outside of just picking Zilean, but starting to increase the skillean of him as well.
Firstly, smartcasting. Being able to Q>W>Q an enemy as fast as you can is essential. The faster you can do it, the less time they have to move away and back under their tower, or decide to flash or dash away. Going Q>Left Click>W>Q>Left Click will cut it in situations where you have a couple seconds to play with before throwing the second bomb. But in the lower legions I'm involved with, you scarcely need to be that fancy with it, speed will do you much better.
The other big thing is getting comfortable with alt. Not alt+tab, that's no fun. Using Alt+E or Alt+R allows you to cast the abilities on yourself, without having to click on yourself or mouse over yourself. In a team fight situation, you don't to be mousing back to yourself to speed up, just to mouse forward again to try to stun them. Using Alt lets you keep your cursor in the danger zone, so you can throw bombs faster and sooner.
Same with the ult. Sometimes when you are solo'ing around in norms, maybe there's only one person on your team who needs the save. And that's you. An optimal time for this is when a team decides to focus you, because every time they focus someone else they don't get a kill and they die. If you're going to be the first target in a team fight, try to hit a stun as soon as you can, then alt+ult yourself so you don't have to mouse over yourself in the frenzy of low elo play. If you Q stunned them early enough. you should have your cooldowns all back up for another blast. Landing two AOE stuns in one fight can usually seal the deal.

I wanted to have a chart like for the threats for this, but this will have to do.

Great Pairs:
Jinx
Tristana
Lucian
Jhin
Draven
Caitlyn
Miss Fortune

Good Pairs:
Ezreal
Twitch
Vayne
Ashe
Xayah

Okay Pairs:
Sivir
Kalista
Varus
Kog-Maw

I don't think any ADC pairs poorly with Zilean. Everyone can use a speedboost to kite, a slow to catch an enemy, an AOE stun, and extra GA effects. The ones I've put in the Great Pairs section, I have quite a lot of experience with. They are all champs who can quickly splash a ton of damage on a stunned target, or can provide CC to make it easier for Zilean to land the stun, which then they capitalise off of that.