Hi, today I am going to teach you about the nuking potentials of Lux, the Lady of Luminosity. Before rating my build please try it out in a game first. Note above is only an example of a final endgame build. Up to the rabadons is core, after it is all situational and you should read my items section.

Greater Mark of Insight x9
Magic pen. reds, the bread and butter of AP Casters, need I say more?
Greater Seal of Replenishment x9
Amazing mana regen early game. Some may prefer the per/lvl version but its all opinion. I don't need as much mana late game because I have plenty of it before I recall. These runes give amazing early game sustainability.
Greater Glyph of Force x9
Pretty generic. Great Late game AP.
Greater Quintessence of Potency x3
Even more early game AP for that great harass of yours.

Flash - Who doesn't want flash? You can use it to help land your snare, escape or chase, it's just plain amazing.

Other Options:

Ghost - Same as flash, multiple uses. Get this if you want better mobility to chase/run. (Get this and Ignite if you want, its a great combo)
Teleport - Pretty obvious why you would want this as an alternative.

The first few items are pretty core.

Explanations:

Sorcerer's Shoes - Amazing with its magic penetration. If you want, Lucidity also works but your gonna need a Void Staff.
Doran's Ring - Just a great starting item with its health, mana regen, and ability power. You don't need pots because you shouldn't be getting hit much as Lux. Just farm and harass with your "E"

Situational:

Lich Bane - Great item that gives you even more punch in your combo. With this you can probably 1 hit full health carries like Vayne/Ezreal/Ashe etc... with your combo.
Zhonya's Hourglass - Did you just go too far with your awesome powers and the enemy wants you dead? If they're going that extra mile to go through your team to kill you, get this for its awesome powers.
Morello's Evil Tome - Pretty simple item and a great CD reduction. I will usually get this after maybe Rabadons.
Moonflair Spellblade - Just way too much CC on the opponent team? Get this.
Archangle's Staff - Honestly, I put this here in hopes of telling you not to get this. Getting Tear of the Goddess early just isn't worth your money. Also Lux has fairly long cooldowns so you won't be spamming. I mean its not like your Ryze or anything.

Early Game

I suggest going mid, you'll out range most carries. If your laning try to go with a gap close melee or someone with good CC( HINT HINT SION). I love harassing with my "E" early game. Throw your "E" out if your 100% sure you can hit the enemy (usually always). Immediately follow up with a normal attack if you can, your passive can be deadly. Don't use your skills too much though, just try to keep the opponent at around 2/3 of their health. You can most likely nuke them down at level six. Your main priority is FARMING. FARM GOD DAMMIT. When you can stay behind your creeps, try to throw some normal attacks at the enemy champion, its small but consistent damage. Note this only works on some champions.

Main Combo/You Just Hit 6

If you have got them down low enough, then its time to finish them. Throw out a well placed snare and when you land it throw your "E", laser, normal attack, detonate your "E" and normal attack again. This will wreck them entirely and is probably a guaranteed kill if they started at half hp. If you stall too long, the snare will break and your "E" will miss. Also, try to throw your "E" a tad bit behind the enemy because they're obviously gonna run away when the snare breaks.
Play Video Notice that sleek dodge when he Q's me :D. I did mess up my combo order because I used my laser before my "E". Notice how I throw my E behind him though, because he runs right into it. Also, pay attention to that auto attack I threw out right before my "E" hit. My "E" triggered my passive and that auto attack finishes him off.

This is my first build so please don't downvote me because you think it will be funny. Try it out, if its not working well then it could be your playstyle. When i first bought Lux I never chained skills which was my downfall. Think of Lux as an AP nuke, throw your spells together and immediately one after another. Thank you for reading my guide and I hope you will give me a thumbs up. :)