This is a guide to playing Zilean, Angel style. I see a number of players playing defensive Zilean guides, some with almost no AP, and others trying to stack AP using Mejal's Soulstealer. Most people ignore Archangel's Staff, an item that was made for Zilean, giving him a large mana pool, Ability Power, and mana regen. The following guide can be summed up very simply.

Rush Tear of the Goddess. Get Boots of Mobility. Finish Archangel Staff. Buy Glacial Shroud.

Archangel's Staff is your primary Ability Power producer, and keeps your AP level respectable while building Glacial Shroud/Frozen Heart. Glacial Shroud is gotten after Archangel's to keep you relevant in Team fights, and to help farm.

Item Build:

Starting Item(s):
Sapphire Crystal. 2 Health Potions.
Sapphire Crystal ? Tear of the Goddess
Boots of Speed ? Boots of Mobility/Sorcerer's Shoes
Blasting Wand(w/Tear of the Goddess) ->Archangel's Staff
Sage's Ring + Cloth Armor ? Glacial Shroud

Luxury Items:
Abyssal Scepter
Banshees Veil
Zhonya's Ring
Guardian Angel
Frozen Heart

Reasoning:
Sapphire Crystal makes constant timebombs possible. Tear of the Goddess gives you a large mana pool and some needed regeneration. At level 6, zilean can burn through a large amount of mana in a short amount of time. Boots of Mobility are REALLY good on Zilean. They allow him to gank, farm, and escape very well, particularly in combination with Time Warp. Time Warp on himself makes Zilean virtually uncatchable. The first Timewarp usually takes you out of combat range, and then the boot move speed kicks in. The second Timewarp takes you to the other side of the map.

Runes:
By level 18 you want close to 40% Cool Down Reduction (CDR). I usually go with close to 6% CDR. Combined with 9% CDR via masteries and 25% from a Frozen Heart, puts you at the hard cap of 40% CDR. AP can round out your unused runes. If you're leveling your summoner to level 30, Cooldown reduction is most important.

Masteries: 
The CDR in the Offensive and Utility trees. Cooldown Reduction is the only must have with Zilean. If you haven't hit level 30 yet, the Cleanse Mastery, Willpower (reduces Cleanse CD by 30 seconds is very good), and Strength of Spirit (Increases Health Regen based on Max Mana) in the defense tree can really help with laning. 

Summoner Spells:
The best summoner spells on Zilean are probably Cleanse and Teleport. Teleport is always useful, for defense, ganks, or simply quick shopping trips. Cleanse compliments Zilean's natural escape mechanisms, and is superior to flash in the important cases; Stuns. Zilean is uncatchable, except via slows/stuns. Cleanse answers those problems that flash doesn't, and also lets you contribute to team fights after a silence.

Game Overview:
At the beginning of the game, let your allies know what Chronoshift Does, what it looks like, and why they shouldn't run away while its on them (Usually). Especially at level one, chronoshift has a relatively small duration. Chronoshift wearing off is a bad thing. Make sure people understand that they need to die ASAP while they're wearing the spining egyptian rune things.

Early Game: Zilean is an effective solo, or lane partner. Time Bomb is taken at almost every available level to increase max damage and start farming ASAP. It also helps harass and when combined with Rewind, can deliver a hefty nuke. At level 6, your ultimate, slow, and time bombs make you very difficult to gank. Tear of the Goddess should be gotten ASAP. Followed by Boots of Mobility.

Mid Game: At level 8, you should be able to kill the entire ranged creep row with a time bomb. 2 Time Bombs and well positioned creeps kills an entire wave. Help gank lanes. Timebomb x 2 & a 3 second slow are ridiculous. Ultimate should be used liberally on low health allies. Farm whenever possible. With the exception of the Uber creeps (Dragon, Lizard Elder, Big Golem) the neutral creeps can be quickly dispatched via timebomb. Farming is important because your hero kills are sporadic. If Chronoshift is on Cooldown, spam rewind if you're not currently engaged, readying Chronoshift earlier. Using Rewind before you Recall to base or while you use the shop is also handy.

Endgame: Use Ult to revive allies, spam rewind at every opportunity. Double Timebombing a champion at the beginning of a team fight and then every 4 seconds there after (assuming 40% CDR) helps greatly. Push lanes if you've nothing else to do. Zilean can push a lane up to an opposing tower in almost the time it takes to walk up to it (sadly you can't do much to the lane once your there). Based on the enemy teams composition at this point you should be choosing your final items.
Lots of Melee? Frozen Heart/Health/Guardian Angel
Stuns? Banshees Veil
Casters? Abyssal/Banshees Veil
Want more Damage? Zhonya's

Summary:
Zilean's skills drive him in 2 directions. He wants AP to deal damage and remain relevant at later levels, a LARGE mana pool early to spam his skills and keep his ult up. Most heroes can rely on hero kills to supply them with gold, however, later in the game, after level 10, Zilean rarely lands the killing blow. Instead, focus on farming, pushing, and giving your team longevity, and know, secretly, that your team is winning team fights, ganking, and pushing due in large part to your contributions.

Appendix.
Passive:
Heightened Learning - Increases Experience gain of all allied champion by 8%.

Active:
Time Bomb - Places a bomb on any unit, allied or enemy. After 4 seconds this bomb will detonate, dealing 90 / 145 / 200 / 260 / 320 (+1 per ability power) magic damage to all surrounding enemies.
Cooldown 10 seconds Cost 80 / 95 / 110 / 125 / 140 Mana Range 600 

Rewind - Reduces all of Chronokeeper's cooldowns by 10 seconds (including Rewind).
Cooldown 36/34/32/26/22 seconds* Cost 80 Mana Range 600 
Time Warp - Slows an enemy champion's movement speed or increases an allied champion's movement speed by 65% for 3 / 4 / 5 / 6 / 7 seconds.
Cooldown 20 seconds Cost 110 Mana Range 600 

Chrono Shift -Marks the target with a protective time rune for 15 seconds, if the target would take lethal damage they are instead transported back in time regaining 500 / 750 / 1,000 (+3 per ability power) of their health.
Cost 80 Mana Range 600

Zilean's abilities make him an effective ganker, farmer, and support hero. During the early game, Zilean is a force to be reckoned with, as his slow prevents escapes, and Time bomb spam pushes the lane, denying enemy heroes gold, and can cause hero kills underneath an enemy tower with little risk to the clock man himself.


Ability Selection:

1. Time Bomb
2. Rewind
3. TimeBomb
4. Time Warp
5. Timebomb
6. Chrono Shift

After level 6, your priorities, from greatest to least.
ChronoShift
Max Timebomb
Rewind
Time Warp

Rewind is taken early to increase Chronoshift's , as well as Time Warp's, uptime. Exchanging 1 or 2 levels of Chronoshift for Rewind is acceptable, as Time Warp on an opposing player for a 5 second slow is REALLY good. More than 5 seconds is really overkill. The situations early when a 6 or 7 second slow would result an otherwise impossible kill are very few.