Zilean can be played as a mage or a support.
Since his Chronoshift (R) is a life saver, his Time Warp (E) is a life saver and his Rewind (Q) helps to get your (R) and (E) ready quicker, I assume he's more a support than a mage. And what about his passive Heightened Learning ? Junglers will love you.

Nevertheless we'll get some MagicPen for his Time Bomb (A) and Ability Power for both his Chronoshift (R) and Time Bomb (A) to be a threat.

Heightened Learning
No comment, it'll help the whole team to reach their lvl6 quicker. And your jungler'll be more comfortable.

Time Bomb
It's as effecient if you put it on your allies than your enemies, depend of the situation.
Put it on your tank to engage a teamfight can be usefull.
Good to know : When fighting against another Zilean, Time-Bombing your own allies will disable their bombs

Rewind
What to say... double bomb, double time warp (increase your speed/decrease their of your enemy)
Lvl 18 it'll able you to get your Chronoshift every 45s if you use it as often as possible.

Time Warp
Excellent gank or flee ability.
I use to increase my speed but sometimes it's better to reduce their of your enemies. If he's tower diving slow them down then flee or run around depending your amount of HP.
If your chasing and able to put it on the enemy it's better then your mates can reach him and he'll be longer to get to his tower/mates.

Chrono Shift
What to say ? Just be reactive ! Since it give you back the same amount of HP, you can wait the "borderline end" to use it. (Before it used to give back the amount of HP the same when you used the spell)
More over, it's good to deny Karthus's ulti : Requiem, Caitlyn's Ace in the Hole or Mordekaiser's Children of the Grave

He's a "mana-ovore" then we'll need Greater Seal of Replenishment as glyphs.

In my opinion his cooldown reduction is one of the most important stat so I chose to get Greater Glyph of Cooldown Reduction as a seals.

Most of supports do some magic damage, then Greater Mark of Magic Penetration is the best option for the marks.

Finally as most of supports he's a bit squishy, then Greater Quintessence of Health for quints is our best option.


Other runes possible :
I always choose flat runes because according to me runes make the difference early game.
Later on, for exemple +9AP when you have 350 it's ridiculous.

For the coldown reduction Sorcery and Intelligence are the must have.

To be a threat as I said in the intro Mental Force and Arcane Knowledge are more than usefull

We are mana-ovor then Meditation and Expanded Mind are good.

We are a support, here some inconvenient :
we'll lack of gold, then Greed is our solution.
we'll have to ward then Scout is good.
We're late on xp then Awareness and Sage should help.

To use our summoner spells the best way we'll need Summoner's Insight and Mastermind

I can't see other summoner spells than these :

: As you are a support you need to chase the jungler everytime your Clairvoyance is up. Are they killing the drake ? What about Nashor ? There must be one Clairvoyance in your team and since you're the support...

: the best escape spell ever, jump over trees or rocks...

We are support but without heal.
What's the best way to defend ? ATTACKING !
That's why I chose to maximize the Time Bomb

Then the Time Warp we'll help to run away or to chase

Early game try to harass with Time Bomb the more you can.

If they are cautious, hide in a bush, Time Warp yourself then run over to put your Time Bomb

As you know you're a support then do not last hit, and harass the most you can.

Later on try to be in every teamfight to be efficient, that's why Mobility Boots can be usefull, nevertheless I prefere Sorcerer's Shoes to get an efficient harass.

Of course your build can be different in every game, but according to me the Core Build is always the same.

Here is my buid :

As we are support we need gold and regen mana. Then get Philosopher's stone as soon as possible.

Catalyst the Protector is a good way to get some extra mana and mana regen (same for hp since you're squishy)

Soul Shroud will help you and your lane-mate with the mana and the cooldown reduction but finish it after boots otherwise you'll be too slow

Then you should get some extra AP so get your Rod of Ages and your Rabadon's Deathcap

LATER finish your Shurelya's Battlesong to keep your Philosopher's stone as long as possible, it's a good gold gainer.

Finally get a Guardian Angel and you'll never be focused again (what's the point to kill 3 times a support ?)

Try to get wards for nashor and drake all the time.

Ask your mates jungler, carry AD and solo top to get Wriggle's Lantern. It helps them for a good survivability and wards are the way to get map control and to win !

Other/Situational builds:

You won't make as much damage as the AP build but you shouldn't die :)

You'll be squishier but you should make great damage

You'll make some damage and you should be everywhere and help AP mates a lot !


Items I choose not to pick :
Morello's Evil Tome : I already get 40%CdR with other items more usefull as a support
Ionian Boots of Lucidity : the same, 40% CdR already
Zhonya's Hourglass : the active is not as good as it looks like for Zilean
Heart of Gold : gold is good but we won't change it to Randuin's Omen so what's the point ?
Kage's Lucky Pick : the same, gold is good but Deathfire Grasp for a support ?

Here we are !

40% cooldown reduction done !
285 AP done ! Then you got a 585 damage Time Bomb and your mate will get 1600HP after your Chronoshift

After a quick calculation I found you can get your Chronoshift ready every 45s instead of 180s thanks to your cooldown reduction of 40% and the fact that you're spamming Rewind everytime it's ready

To chase don't forget to Time Warp the enemy, then Rewind and Time Warp your mates and active your Shurelya's Battlesong.

With 10%( Arcane Knowledge )+28.5( Sorcerer's Shoes+ Greater Mark of Magic Penetration) Magic pen, enemies without Magic resist should be around 0 so your Time Bomb should make a lot of damage ! (around 585 !lvl 18)

To tower dive you can send a mate of yours with a Time Warp and a Time Bomb "Surprise!"

Do not forget to Time Warp your mate after he get a Chronoshift otherwise he'll die again :)

I took a lot of information from other Zilean's builds so I'd like to thank their creators : Mowen, Gabriex, unSupport....

If you have some advice or see something wrong just tell me, I'm open minded !

I'm french, so please don't be mean about my english !