Why should you follow this guide?
This guide is going to make your opponents rage. It's going to make them hate you. They are going to rage in /all chat and call your team a bunch of *******. All the while, you're going to trolololol around the entire map and make sure your team has a clear and massive advantage.

Zilean is a great zoner, he's a fantastic denier, and his role with this build on the team is to give your team an advantage in gold, kills, and utility.

Magic penetration reds are amazing on any caster, and that holds true for Zilean.
The mana regen yellows are going to help you keep your mana pool up which is crucial for staying in lane and denying your enemies farm and experience.
AP blues are going to give your bombs a little extra oomph
AP Quints are just going to further the damage your bombs do.

Passive: Heightened Learning:Increases the experience all allied champions gain by 8%. This is not in effect while Zilean is dead.

Heightened learning is amazing for your entire team. It has no range, it's just a global experience boost for your whole team while you are alive. Part of your role as Zilean using this build is, like I said, giving your team a huge advantage in both gold and experience. Zilean's passive does just that. If you do your job and deny your lane, you're going to vastly outlevel your opponents.

Q: Time Bomb: Zilean places a time-delayed bomb on a target. The bomb will detonate after 4 seconds, dealing magic damage to all surrounding enemies. The bomb will detonate immediately if the holder dies or if another bomb is placed on them. Enemy holders will take 1, 2, 3 extra true damage gradually before the detonation.

This is your only damaging ability. Lucky for you, it's incredibly strong, and with your W (Rewind) you can cast it twice, immediately one after another. Notice that when a second bomb is placed on top of another one, the first immediately explodes. So your main damaging combo is Q-W-Q, and that is a massive nuke. Your bombs are really versatile, they can be placed directly onto opponents, onto their minions, and even onto your allies. If you've pushed your lane up to the enemy tower, you can toss your bombs onto your own minions and continue to harass from a safe distance. If you've got a melee/assassin who's got a gap closer, throw your bomb on them right before they go in to increase their burst. Your bombs also explode when the unit they are attached to dies. If there is a low enemy creep near an enemy, double bomb it for an immediate two bomb nuke.
Additionally, this spell is great for zoning. Toss one or two onto an enemy every time they get close enough, or even onto their creeps to keep them out of experience range. Recently in a game, I was bot supporting Caitlin. We did such a good job of zoning our enemies out of lane that without even getting kills, we had taken their tower at 8 minutes in. When we were level 8, they were level 5. I can't even begin to explain the huge advantage this gives you.

Q: Rewind: Reduces all of Zilean's other abilities' cooldowns by 10 seconds. Rewind does not affect itself or summoner spells.

This is an amazing spell. On paper, it doesn't look to be all that amazing. But with max CDR/max rank, it has about a three second cooldown. This is what makes Zilean amazing. You can throw unlimited bombs, you can revive a teammate every 20-30 seconds, you can infinitely speed boost yourself, and sometimes even yourself and an ally. Or you can permanently slow an enemy. By the end of your game, spam, spam, spam, spam the hell out of this spell. It will help build your tear, and you can use your ult so often. I've had enemies complain that I was hacking because I used my ult twice in such a short time frame.

Q: Time Warp: Zilean slows an enemy champion's movement speed or increases an allied champion's movement speed by 55% for a few seconds.

At level 18, like I said, using your W and your CDR you can have a permanent +55% movement speed, or cycle it through all of your teammates to move your whole team quickly through the jungle for an easy gank or surprise ambush. This spell can save your life if you get caught in a bad position, or save an ally's life while they are running away. Conversely, it can secure you a kill since it's basically an exhaust, or help your carry catch the runner. Deciding who to use this on and when will vastly improve your game, but this is a skill that comes with experience. Using this skill on yourself, combined with your boots of mobility, is going to get you around the map EXTREMELY fast. Be everywhere. Thwart every gank.

Q: Chrono Shift: Marks an ally champion or himself with a protective time rune for 7 seconds. If the target takes lethal damage during this time, instead of dying, they will be untargettable and remain in stasis for 2 seconds and then they return to life regaining health.

This is the move that's really going to make your enemies rage. Deny them gold by thwarting their ganks with this. You or an ally can tower dive in a situation you wouldn't normally be able to. You can bait enemies with this move. This move WINS team fights. If they focus your carry, ult him/her. While they are in stasis for a few seconds, the other team will change focus, and then get obliterated from behind when they get back up. Every time your ult is successful, that's a ton of wasted resources for your enemies. With just a little bit of AP, this spell brings most people back to life with at least half health, and if you're doing really well and decide to go for more AP, sometimes even to full health. That is massive in a team fight, and this spell is what is going to give your team the advantage. Remember, spam that W so you can use your ult all the time.