I'm going to share my personal favorite build of Zilean. Let me note that I've had a ton of experience in Zilean, and while I don't do ranked, I still concider myself a very good Zilean.
This build is for pure support.

Pros: Almost no one will die if their smart enough. And you'll be able to slow or haste two targets on a constant upkeep if you go frozen heart. Fantastic survivability, not the best, but it's pretty good. Not very squishy, a little tanky in fact.

Cons: Very gold reliant, you need to always be with a team mate to ensure your getting assists, otherwise you'll be seriously lacking. Requires very very good positioning so your not in a bad gank position. Dependent on team's intelligence.

When you start the game, you're going to want to begin with the pendant, as your skills cost a ton of mana, you'll only need the health potions. On your first return at least get the basic boots, then go for the chalice, as this will help with both mana regen and magic regen, and will help prevent us from getting too low on mana.
Building the boots of lucidity and the kindle gem will help massively in out CD, as we need to max it in order to be maximum troll. The mana manip will build into the soul shroud, which we need as soon as possible, but after the goddess tear (This is a key item!). As soon as you can afford the shroud, go for it, and if you have the money, the Archangel staff, but if you don't, grab some cloth armor to begin building your aegis.
Once you have all that, you're pretty much at full build. If there's a ton of CC on the opposing side, grab a Banshies veil, other wise if there's a lot of physical damage, build into the frozen heart (Which is more desired)

I chose teleport because when you do die, you want to be able to immediately get back into the fray with it. If you don't like teleport, grabbing cleanse is the next best choice to avoid ganks.

Why clarity? I hear people say it's a noob skill for people who can't manage mana. I call that bull. It's a really good support skill to help anyone who uses mana able to stay in the fight just a little longer. That small bit of extra mana can save everyone. If you don't like clarity, grab flash to better avoid those nasty ganks.

Pure support Zilean is difficult to pull off, but when you do pull it off right, here's what will happen:

1. Your team mates wont die

2. Almost nothing that gets near you and your team will be able to get away

And

3. Enemies will never be able to catch you or allies.


Knowing who or when to haste (Buff ally) or slow (Debuff enemy) comes only with experience, and changes drastically on the situation, but here's a few tips:
* If the enemy is within or can be reached easily, you should be slowing them down rather than hasting, because if the enemy is slowed, everyone can catch up.
* Be sure to haste the ally closest to death, unless there's only a single opponent whom you know can't damage unless they're within a certain range.
* When you have both your tear of the goddess and chalice, don't be afraid of using your mana to haste your allies into battle, as that will only further help yourself.
* Don't be afraid of hasting yourself, you're important too, and if you die the rest of the team will fall apart.
* Don't get cocky just because you have a resurrect. You only should use it when you need to, not when you want to. Using it just because you can will result in failure more often than not.
* Use time bombs to pop bubbles (Remove the banshie veil spell protect) so your allies can hone in, and so you can use your slow.
* (Troll) Your time bomb actually does damage as you lay it onto an enemy. The first second deals 3 true damage, then 2, then 1, then 0, then BOOM! You can use this to cancel Miss Fortunes passive, or prevent a stealth unit from becoming invisible for an extra 3 seconds.
* Use your bomb! It doesn't do a lot of damage, but it puts pressure on the opponent, and it may be that little bit of damage you needed to finish them off, but be careful with using it too much in the beginning, as it'll leave you manaless.
* Don't be shy in using rewind, it's our bread and butter in order to repeatedly slow and haste, and bring back our ultimate.
* (Troll) Once you get max CD, you can easily maintain two slows or two hastes. Things can quickly turn for your and your teams favor when you get maxed out CD, and you can prevent an enemy from catching you or running away too quickly when your alone, allowing your team to easily catch up.

I dive deeply into the defensive masteries to help a lot with early survival. I take up mercenary because when your getting a lot of assists it quickly stacks up, and allows you to build faster.
Enlightenment is used mainly for if you don't think you can or will build into the frozen heart. IF you don't intend to take it, take evasion instead, every bit counts.
I personally like the hasted recall. I'd go as far as to say it's vital, as it allows to avoid ganks if you know the enemy is coming and you can't get away within 5 seconds. Otherwise pick up summoners insight so your clarity is better.