Some might think this is a silly idea that wont work. I have proven those non-believers wrong quite a few times myself. I do it and get a response something like: "WTF, AD ZILEAN? FKN TROLL", then by the end of the game they apoligize (those of you that like wierd builds probably know the sensation when they do). But when you think about it, why not?

Focus on high damage each hit and move speed. Your aim is to be running around everywhere, dodging skillshots and poking a lot, due to your high range. You are also almost impossible to escape once they start running, (except possibly if they go over a wall).

Items also viable:

Frozen Mallet
Zephyr
Bloodthirster
Maw Of Malmortius
Runaan's Hurricane
Zeke's Herald
Last Whisper
Manamure/Muramana

Why level speed boost first? Like i said in the items chapter, speed and range are your vital assets. The speed boost is also very versatile, etc. you have a Blitzcrank supporting you. You can speed him up so he can grab, you can slow the enemy for an easy grab, you can catch up if he is ahead of you, you can escape yourself while he runs with overdrive. Many possibilities. Then you level rewind for decreased cooldown on the cooldown decrease ability (lol).

You need flash. Period.
If it's a ranked game or draft pick, improvise. They have lots of CC on bottom lane? Take cleanse! You need sustain? Take heal! They have nuke? Take barrier! (I usually prefer ignite though.)

Main pros:

Long range
Much poke
High speed (with boost)
Functions well with a good team
Versatile

Main cons:

Relatively squishy
Often vulnerable to gap close spells (jumps, dashes)
Hard to play

Playing this build in Solo/duo queue can be tough, people will very likely rage on you because they dont understand the idea of AD carry zilean. They might leave or troll, so i would'nt risk it unless you're first pick and have a friend with you to back you up as a support, or in a full ranked team. You will at least definately surprise your enemies and they might underestimate you.

Zilean is a very unusual pick as a carry, but strange builds that work are really fun (jungle or solo top Blitzcrank, jungle Ryze, AD Malzahar etc.)! It is relatively easy to fail this build, but when played right it is plain awesome! With his long range, speed boost and ulti, AD Zilean is very viable. You will need the items if you want to do any good, so make sure you farm a lot and preferably get all the kills an your lane. A good support will make things easy for you. Poke 'em down to 60% hp, then engage with full force, and if you have ulti, you come out of this with at least half your hp and probably 2 kills. Carry and support your team at the same time with your ultimate, speed boost and passive. Go nuts.

Dont waste your time, or time will waste you.

(Counters: Kog Maw!!! Ezreal, and Caitlyn can be tough)