as the title says

buy AP items
maybe a little support if your team needs it
spam time bombs
???
profit

Try this Zilean Guide

zilean needs to be survivable and well as have a large mana pool to be useful in longer lasting fights

http://tinylc.com/Dv

that guide has some really good zilean info
enjoy

as for my personal build, i like
CDR boots, Aegis, Arch angels as a core

moving on to late game items depends on what you need
items like deathcap with a more AP oriented build help your resurrects heal for more, while a BV is great if you are getting focused. soul shroud is a great late game item as well, as it puts you at CDR cap most games and gives team mates CDR and Mp5 as well

9/0/21 (obviously)

Flash and ignite (flash is my escape crutch; Bomb/rewind/bomb topped with Ignite is certain death)

Mpen red
mp5 yellows
Ap/lvl or mp5 blues
Flat Hp quints

Core items:
Catalyst, Sorc Boots, Morellos
Upgrade Catalyst to BV
Then get Zhonyas
From here you have enough AP for your bomb/rewind/bomb combo to do 75% dmg to most champs, so build more for total annihilation or build more survivability.
More AP items - Abysall Secpter, Rylais, Deathcap, or even Mejas
More survivability - GA (two deaths are hilarious), QSS, look at enemy team and determine MR or Armor

Buy blue elixir every return trip
Buy wards for map awareness

tyvm

leaguedb.com gogogo

Stack AP, revive your irelia and trolololol.

I'd say focus more on being beefy and CDR than AP as Zil.

Zil with no AP, or even items for that matter, is still amazing (a level 5 double bomb clears entire waves of minions even w/o AP). It's getting that rewind/ult CD to a minimum that's crucial, as well as not dropping like a rock instantly in team fights so you can hang around to permaslow/speed and eventually revive.

guardians angel + ult + soraka = other team raging