Greetings! I happen to be a Zilean main who may or may not actually be that skilled with Zilean. But let's just say, I've murdered quite a few people many times with Zilean in the middle lane. Occasionally I will take him top, but it is... Not as effective. So let's go through why you should play the Zilking mid:
Provides utility to the team
Losing lane is ok since you have your ult, revive that ****en carry
Has surprisingly high escape thanks to E
Thanks to 5.21 changes, you can help level up your jungler and other lanes while getting ahead in xp in lane! 5.23 guarantees you 15% of Experience stored, meaning you get more Experience even if you only grant 15
Can become an unstoppable force when fed
****EN HILARIOUS TO PLAY WHEN FED
HOLY **** EVERYONE NEEDS TO PLAY FED ZILEAN
Best laugh in the game
Squishy as hell and can be bursted easily
Hard to land bombs
Hard to be effective with, even when fed compared to other champions
High mana costs
You might be weak willed and unworthy to hear the laugh

Who can I level up?
This lets you level up an ally and provide yourself with the XP you award them. This is a two way aid letting you get an XP advantage over your opponent and your ally over theirs. When looking over someone, there will generally be a circle around them. When the circle is fully golden, right click them and after a brief channel you get to listen to the glorious sexy laugh that is Zilean. Constantly look around the map at your allies to see if you can level them up. This is most useful with the jungler since you can boost the XP gain they receive. If communication with the jungler is lacking, look for an ally you can boost and go gank their lane giving you and them bonus XP even if the gank doesn't accomplish much.

Start
You're an AP mid laner. We use one mana potion cos that **** expensive early. Golly gosh darnit Rito.
Core
Morellonomicon
You see... I've thought about this one. Seraph's Embrace provides more AP and mana overall, however it lacks CDR which is direly needed to reduce the ult time. Also, Seraph's Embrace requires time to eventually build up into... Which we can't be having any of that. All in all, I rush the book first for the mana regen and CDR.
Ionian Boots of Lucidity
Help you go at very hih speds and reduces cooldowns.
Banner of Command
I honestly think this item is really good. If you're not fed and ahead, I think this item will work far better than a rabadon's killcap. And even then, it is a major contribution.
Rabadon's Deathcap
666DAMAGE666 6x Rabadon's is a good build in itself, so why not pick one up!

Now out of the core
Zhonya's Hourglass
Very nice item to have, however it leaves you immobile. Very nice for watching as a bomb ticks down on your foe.
Guardian Angel
Are you an unstoppable force rampaging across the battlefield? Do you want to blow **** up and never die because they fed you to the nine hells? This is for you!
Luden's Tempest
Good if you're stomping.
Void Staff
Use this if magic resist is a real issue.

Before we start, there are a few things I should mention. ASSIGN YOUR ULT TO SELF CAST ON YOURSELF WITH A SINGLE BUTTON HOLY ****! YOU NEED A PANIC BUTTON. ALT + R IS NOT SUFFICIENT. I HAVE ASSIGNED MINE TO H, IT IS MY PANIC BUTTON! WHAT IS YOURS?!

Now onto the good stuff
Bread and butter
Q W Q is your core combo. You pull that off, you're doing good. There are a few ways to go about this combo and I will list them here:
Generic
In general, you just want to Q W Q. This costs quite a bit of mana so be prepared to deal with that and only go in if you think you can get it. Use this when being chased, when poking, when ****ing *****es, when doing homework, and whenever.
Accuracy
If you want to hit, E your target beforehand. This slows them to a crawl and makes it super easy to hit your Q W Q combo. This increases the cost EVEN more so use sparingly.
BOMB WISELY
If you're ulted, and are about to die, don't stun the ******** target. RIP me when I stunned the Yi during his attack animation. Make sure to DIE when you need to.
Allahu akbah tower dive
This is perhaps the greatest Zilean strategy that will almost guarantee a kill if the target is low enough. Q yourself, E yourself, and run at the target. Ult yourself if necessary. If they kill you, you explode. If you die, you don't die. If they're under a tower, doesn't matter. Flash if you need to. Have fun.
Chases
Zilean chases. Beautiful. Q W Q and E. Q W Q and E. Repeat until they give up. Chase them when they run. Nobody runs from Zilgod.
Teamfights
You can really shine here. During teamfights, you can provide an AOE nuke stun. This can easily change the tide. Also, you provide massive utility with E. R is great for reviving the carry or screwing over enemies like Katarina.

Ignite
Hahahahahhahahhahahhahahahhahhahhahhahhahaha burn ****. Secure kills. /laugh. Good mid.
Flash
Ult, flash, E and you're free.
Teleport
Only take if you're top. Perform sp00ky ganks.

Try to last hit EVERYTHING. It is HARD with Zilean early game, but once your QWQ combo can clear an entire wave, you're set. Early game, try spamming laugh to reset your autos. It annoys the opponent and can help time your autos.

Zilean is one of my favourite champions because he kit is just ******** so fun. It's also effective, no matter if Zilean loses his own lane. Whether you want to murderbone or save your team, don't play Zilean support or without the Groovy Zilean skin(New splash, groovy zilean is dead), otherwise you're dead to me.