Zilean is not a support. He's a support mage, so build him like a mage.

Runes: mrpen marks, because they're the only decent mage marks.
seals are probably best as mana regen, but armor could work too.
glyphs and quints should be AP, so your laning is super strong.

Masteries: 9/0/21 is best, because there's not much other options for mages. All the masteries here should be common sense.

Summoners: Flash/Ignite, because flash is amazing and ignite secures you those kills when you bomb + ignite.

Items: Start Boots and 3 Health Potions, because that way you can harass the enemy like crazy and get out relatively unscathed. Also if the enemy is playing conservatively, you can run in like a speed demon with E + boots and they won't be able to escape your harass.

Here's the total item build:

catalyst the protector
Sorcerer's Shoes or Ionian Boots of Lucidity (it's your choice, but I prefer the sorc shoes for more damage. Your rewind should be enough CDR in general)
Rod of Ages
Rabadon's Deathcap

after this you could do virtually anything, and it largely depends on what your enemies are doing:

Will of the Ancients
Zhonya's Hourglass
Void Staff

...in no particular order. Other options, but less optimal/more situational, include:

Moonflair Spellblade not a bad option, just buy early on. situational.
Rylai's Crystal Scepter the slow is virtually useless, tbh, but health + lots more AP than you can get from any other item at this stage.
Abyssal Mask not a bad item at all, just don't use with Void Staff. Also not optimal because the enemy may be faar far away before your bomb goes off, thus making the aura useless for your damage.
Morello's Evil Tome or Deathfire Grasp might be useful, if you didn't get IBoL, but both highly situational. DFG can help boost your damage a lot.
Archangel's Staff might be good if you get an early tear, but that changes early game a whole lot and delays your heavy AP way too much. Only good if you 1. buy tear early and 2. if the game lasts long.

There's also the option of buying pure defense, which isn't bad at all. It just depends heavily on the enemy. Frozen Heart might be good if you haven't capped your CDR yet. Banshee's Veil is always a good consideration. Quicksilver Sash can really help you make sure you get your ults off.

The point of this build is to basically make sure you have as much AP and damage as possible, because your ult is more useful with AP (gives a whole second life, instead of a measly Guardian Angel type revive), and your bombs won't scale well into late game unless you stack AP hardcore. RoA is to make sure you have enough mana - this, runes, and blue buff should give you enough in general. If not, consider a BV or FH late game.

Play zilean mid. Bomb the ever-living **** out of the enemy any time they try to take creeps. If you end up taking damage, just use potions. Rinse and repeat until the enemy is low health. DO NOT double bomb early on. It's a huge waste of mana. Use mana only on single bombs, until extraordinary circumstances present themselves (gank from either side, aggressive enemy, potential to flash-kill enemy).

Get blue buff from jungler, and past lane phase try and land bombs on anyone close enough. DO NOT DIE YOURSELF. Your ultimate should be used on an important ally (e.g. a big initiator/bruiser, or the AD carry. Basically anyone dealing the damage). If you take a lot of damage, don't recall - sit back, wait to ult an ally, and bomb enemies if they get close. Just phase into more of a support late game, since your bombs won't do enough to be main source of damage (though landing two on an Ad carry can do a lot to them), and you'll be very useful for your ult/speed.