My first guide so I welcome your advice and constructive criticism.

I'm going to attempt to explain why Zilean is such a viable and awesome choice for Twisted Treeline. I know nobody wants to read a lot so I will keep it brief.

Keep in mind, he can very easily be a very terrible choice depending on your team comp. I build him AP so he can nuke with his bombs but he is still very much a support so you need tanks or bruisers or somewhat sustainable champions on your team.

I choose flash and clarity which seems to be very popular on Zilean.
Flash is almost always essential for champs.
And Clarity is very nice for someone as mana hungry as Zilean.

Ignite, Exhaust, Heal are also viable but in the long run Flash and Clarity are the way to go.

Do what you want here it is all about preference.

I like to be faster than everyone else so I go with swiftness quints.
Marks for magic pen and seal and glyphs for a little bit of defense.

The 21 points in offense are obvious choices. I choose utility rather than defense because the way I play I avoid taking damage as much as possible.

After you have finished my build order get some support type items... either defensive or offensive items with auras to support your team.

Frozen Heart
Abyssal Scepter
WOTA
Zeke's Herald
Aegis of the Legion
etc...

besides your R your Q is clearly the most important skill. This is your damage for poking and for team fights.
Late game team fights your W becomes spammable making your Q spammable so you keep placing those Qs on the focused enemy. Pop clarity when you need it and just continue placing those bombs.
Your E is for slowing the enemy or speeding up an ally.
Your R is quite evident, saving a teammates life or your own. Pay attention with this ult. Don't waste it on someone with Guardian Angel up. And most importantly put this on your teammate that does the most damage if you can.

The amazing thing is that after team fights that you have won you can spam your W in base wasting no mana and having your ult ready really soon. Of course this is only true if your are not trying to push lanes and take advantage of the enemy team being dead. Typically its not your job to be the pusher but sometimes that's your only option.

Pros
His bomb becomes a nuke.
A slow and a speed up.
A lifesaving ultimate.
W makes his Q(nuke) spammable.
Can own in team fights if not focused.
Doesn't need too much farm.
SO FUN!

Cons
Can be shut down in team fights.
Can't clear minion waves effectively.
Q is his only real damage ability.
Needs a good team to be effective, weak team - weak zilean.

To sum it all up Zilean is a very fun champion for 3s.
He can support really well even when built for AP.
His Q becomes a nuke and can be easily spammable.
To play him most effectively run up, drop bomb, run away, repeat.
In team fights stay close but avoid damage, all while dropping bombs on the enemy being focused. Use your ult to save an ally and win the fight with no problem.

Play Zilean effectively and you will be a game changer for every team fight.

tl;dr
Drop bombs, slow enemies, save lives, win games!