Hey there to everyone, I've decided to make this build as I really like Zilean and would like to share my way of playing him with you. He's recently became even better, after they have buffed mages and generally AP characters a few patches ago, and I really think that my build works best with him, so - there we go.

These are the runes that I have for him. Some people may argue that I should get magic penetration, flat HP quints etc, like every mage does - but so far it seems like those pure AP give him a really nice burst on early levels, and I can easily kill people with 2-3 bombs in that part of the game, so later I can get fed. For quints I chose the flat ones, as 2.5 AP (difference between flat and per level) isn't a big deal over 18 levels, and for the rest I've got the per level ones, as you don't lose so much with them as you'd with flats.

I think they say for themselves. You could put some points some other way in the Utility tree, if you picked different spells, e.g. Flash instead of Ghost, or would like to be rather dependent on the buffs. Still, those work best for me, I guess.

I begin with Doran's Ring, as it early gives a nice burst of AP, some HP (remember we've got no quints for that) and a bit of mana regen, which is always useful.
Then I go for the Tear of the Goddess for yet more mana and mana regen, so we've got more to work with. Immediately after that rush for the Boots of Ludicity, which would give us some less cooldown time on our precious skills.
Then you'd want to turn your Tear into an Archangel's Staff for some AP burst, and eventually get a Soul Shroud later, for some HP, even more CD reduction (39% total, all you need) and additional benefits to your team. Then, for another AP burst, get an Rabadon's Deathcap.
Finish off with 2 RoA's, that'll give you increased HP, even more mana to work with, and yet another AP burst.

Time Bomb > Rewind > Time Warp
Exceptions: Ultimate whenever possible (6,11,16), Time Warp 1 point on level 4 so you can use it, just in case.

You should be harrassing early on, so you can get your precious money from eventual kills. If possible, you should go mid, as it's rather easy for you to win a 1vs1 with most of the characters. Q>W>Q when fighting, E>W>E for retreats or chases, and if someone tries to gank you, just ulti yourself. You should be able to win 1vs2 fights or sometimes even 1vs3, if you're doing this well. Remember, you've got a level advantage over the other lanes, and over your lane opponent too (most of the games, people need to buy potions all the time just to stay on lane with me, and spend more time in the base). If your opponent is low HP somewhere, don't be scared - time wind yourself, plant 2 bombs on him, ulti yourself if the turret is going to get you, respawn, and be glad you got a kill. You should use EVERY opportunity to get a kill, even if you're going to die yourself. Zilean is a character that's beastly in early and mid game, so recently I'm trying to harrass my opponents so much, that they'd surrender on 25. Surprised? Works for me in 2/3 of the games.

If your opponent likes to sit under his turret, don't be shy and use your bombs on the minions. You got to get your advantage and money somewhere, and if that's not on players, that'll work best. Just today I had a game where I was 0/0/0 for over 20 minutes, but I had over 120 minions killed than everyone, so when the teamfight phase began, I've went legendary in one run. Result? Surrender mentioned above.

Also remember that your ulti is beastly. If you have a good carry in the team, someone, that is getting triple kills all the time, the opponents are going to RAGE at you when he respawns over and over. That's your job - make them mad. Zilean is getting worse with every minute of the game, so make them rage, make them feel beaten up, make them SURRENDER.