This is how I play Zilean. You don't like it, you can find another guide.

Squishy Zilean to Zilean the Chronokeeper; this guide will show you the difference between the two of these characters. One is soft and squishy, and the other... well admittedly, he's also soft and squishy, but he deals far more damage.

Zilean is not famous for attack. No. He's far more viable as AP. So the runes you take will reflect this gameplay.

Greater Mark of Insight: They will build Magic Resistance. This will fix that... but not as much as Void Staff and Sorcerer's Treads.

Greater Seal of Regeneration: Zilean doesn't have a lot health or armor, so the answer is Health Regen.

Greater Glyph of Force: Ability power is really powerful, and it will become much better late game.

Greater Quintessence of Potency: Give this champion Ability Power. Cause champions love Ability Power.

Archmage's Savvy: Yay! Free AP! Woo!
Deadliness: This 1 is filler. But chance of dealing double damage? Sure, why not?
Sorcery: Because CR is pro. Also, spamming Time Bombs can make people cry/rage quit
Archaic Knowledge: Magic Penetration is amazing. People will build Magic Resistance against Zilean. This will fix that.
Good Hands: This filler point can make all the difference in a Classic Game. The time you spent dead could have been spent defending the nexus.
Perseverance: Again, increased mana regeneration is great early game.
Awareness: Increased experience is an easy way to stay on your friends level and take an easy victory because your team is level 18 early because of your passive.
Meditation: Even more mana regen for early game.
Utility Mastery: When you grab blue buff, you'll want it for as long as possible.
Quickness: You don't want to be caught in a gank, so you'll want to move as fast as possible.
Blink of an Eye: What caster/supporter is complete without Flash, so pick this up for more of instances of Flash.
Intelligence: "Lower cooldowns for my abilities. The master of time is pleased"
Mystical Vision: Cause no team is complete with out knowing where a gank is gonna happen or where the jungler is so we can destroy him.
Presence of the Master: "Lower cooldowns for summoner spells? The master of time is pleased."

Meki Pendant: This is for early game laning. You can also take a health pot to keep health up.

Tear of the Goddess: Now you could have taken a Sapphire and Ruby Crystal and gone immediately for Rod of Ages. No. That comes later. For now just be patient and take your free mana like a man. Or woman. I can't see through this screen.

Boots of Speed: If you're gonna play, play right. It doesn't matter if you have an ability that slows enemies or speeds you up. It has a cooldown, and their boots don't.

Archangel's Staff: Now comes the fun. You've been siding mostly on the sidelines for the early part of the game. Now it's time for the benchwarmer to take his place on the field. More mana, increased mana regen, and of course, AP based on all the mana you have.

Sorcerer's Treads: They're starting to get wise to your build. Time to counter their counter. Destroy them with increased speed and magic pen.

Rabadon's Deathcap: Time for the item that ties most of your build together. What? You thought that type of thing comes last? Are you nuts? Why when you could get all that AP right now.

Void Staff: They're getting more Magic Resistance. Wow. They're scared of you now. Make them fear you with even more Magic Pen and an additional 91 AP (Rabadon's Deathcap is amazing, isn't it?).

Zhonya's Hourglass: Okay, they got tired of fearing you and dieing. Now they're actively targeting you. Get a better chance to survive by now ever being targetable.

Lich's Bang : Okay. You have more AP. Let's put it all into practice. Each attack you make after you use an ability will now deal bonus damage equal to your AP... that's an additional 786 damage in additional to your Attack Damage (103 @ level 18).

Will of the Ancients: Let's make them cry. You know what? Let's get your teammates in on the action.

Time Bomb. Time Bomb. Time Bomb. This is all of your damage (before Lich's Bane (assuming you get that far into the game.)) You level that skill up as far as you go. Next skill is your Rewind. Take a point in it at level 2. One Time Bomb put onto another will detonate the first. Halve the time, double the damage, double the fun.

Put a point in Time Warp at level 4 just to round out the set. Level it last.

Level you Ult as often as possible. Support Zilean is Support. Also, never use it on yourself if you can avoid (This means if someone and yourself is about to die, the teammate comes first.).

Flash: Already 'nuff said.

Clairvoyance: Because no Zilean likes ganks.

Alternatives can be as follows -

Clarity: More mana for EVERYBODY! YAY!

Ghost: Because everybody loves increased movement speed.

Exhaust: You have to love decreased movement speed/armor/magic resistance. So much slow when you target them with E.

Archangel's Staff plus Time Bomb plus walking away equals epic explosion and tons of gold. Never jungle with Zilean. He never survives it.