Build Guide by

Quick and simple: Tons of damage with Zilean. With that build, you can reach around 1.1k AP, with 1.4k damage per bomb!

Early game: Try to be conservative with your mana. Last hit creeps, with his auto attack is pretty easy, since it's rather quick and have a decent range. Although you got Sapphire Crystal early, if you spam bomb too much, your mana will go wasted easy. Bomb teh opponent if he gets near. With teh runeset, and solo lane, you'll be outleveling pretty fast, which means harder bombs and making your opponent port earlier, also making teh middle turret going down early. In your first port, try to make Tear of Goddess and Mejai. If you're getting fed, do Mejai's first.

Mid game: At this point you should have around 8~10 charges on Mejai's, and boots Lv 5 done. Start ganking, to rack up more gold and finish your items quick. Watch an eye when on team fights to Chrono anyone who needs it. If there're more than 1 going to die, chrono teh carry or heavy DDer, so you can wipe them and keep pushing. If that isn't possible, just retreat and hold up teh turret. Next time you port, finish Archangel's and start another Tear if possible.

End game: If you farmed well, you might be with 2 Archangel's and a Zhonya's done, plus a full stack Mejai's. That'll probably rack you around 500~600 AP, given you've using your abilities pretty often and procced Archangel's/Tear's unique and boosted your mana, which won't be an issue anymore. Try to double bomb when you get into a fight, teh chances you insta kill someone are high. Buy a Brilliance Elixir when you have spare money, and work on a third Archangel's, for more destruction.

About teh Runeset:
9 MPen marks, helps early game;
9 flat AP seals, for early game;
9 AP per Lv Glyphs, for mid/late game;
3 XP Quints, for early game.

"How do you mean XP Quints for early game?", you may ask: Simple, 6% XP from runes plus 8% from his passive plus 5% of utility, plus solo lane will net you a quick outleveling, which means stronger bombs and early game control. With that quick level growth, teh AP per Lv glyphs will kick in faster, offering more benefits than flat. I prefer to use Flat seals instead of AP per Lv because they don't add much (1.8 at Lv 18) and I need some good AP for early nukes/kills, comboing with teh MPens.

For teh Summoner Skills: Flash and Ignite. Ignite for finishing off people, and Flash to get out of sticky situations. NEVER use your Ult if you're sure you can lure them to a dead end and flash over teh wall! It'll be a wasted ult that could save someone else!

For teh Masteries: I go 9/0/21 because of the MPen and CDs, and teh additional Exp on lane, which makes Zilean even more deadly early.

Just a last addend: Play careful! Just go in knowing you can finish off teh enemy and come out alive. Remember you're focused on damage, full nuking. Don't be greedy, share your kills if possible, and win teh game!

And yeah, I posted on anonymous because I'm not bothering to create an acc just for this.
-Sendoh