Note* This is just a build and a small overview of her skills and uses, it's up to the player to use her correctly* This is my initial build for Lux. I don't play her as a support, that's just an excuse some people use in order to justify there lack of kills and many deaths. etc. People then think well hey, Lux has a SINGLE Support skill and 3 other high damaging abilities, she must be a support! well frankly, I disagree. Lux has so much more potential then just getting a **** load of assists. I play her as a full A.P. carry, it's not that hard to use her skillshot's and she's pretty much gonna live do to her shield giving you a lot of shield to play around with.

For Marks I use Greater Mark of Magic Penetration. This is more for the early game usage, but I've found that having a bit of magic pen can determine whether you live or die.

For Seals I use Greater Seal of Replenishment. This is due to the fact that you CANNOT always expect clarity to be up when you need/want it.

For Glyphs I use . Extra C.D. on Lux is always wanted.

For Quints I use Greater Quintessence of Ability Power. With the Doran's Ring Your AP should start of around 32 or so.

Pros:
High Damage
Very Nice Shield
Long (length wise and time wise)
Generally Easy to maneuver around with and play.

Cons:
Squishy (she's a caster go figure :P)
Somewhat Slow
Mana Dependent (I find that her spells soak up more mana then the norm, its just how it seems though)

Basic Mage Masteries, Focusing on cd reduction, ap, and, regen.

I start of with Lucent Singularity. It gives good early game harassment and allows you to farm creeps a lot easier.
Second spell will be Light Binding. A very lengthy snare that will catch your opponent of guard. *NOTE* Not to be used with Flash. If you seriously cant hit her second longest spell then you might want to reconsider playing any champion with a skillshot...( I mean seriously it passes through two things at once, not that hard to land...) Flash is you, main escape ability, since you have the second longest range in the game you don't really need to always be in the teamfight to get some kills.
Then Again with Lucent Singularity.
From there it starts as follows: W, E, R, E, Q, W, Q, R, Q, Q, W, W, R, W, W.

Clarity Is for the extra bit of mana, it will help keep you in lane longer, and help you spam your skills more.
Flash is your main Running away skill. As said before your range is fairly long so you shouldn't have to much trouble participating with the team ;D

OTHER VIABLE SPELLS:
Ghost If you feel that your not reaching the team fast enough, or if you just want more overall map presence.
Teleport The Bane of most backdoor's, a timed Teleport and a good Light Binding will be the death of many foes.
The other spells are just bah, feh, and meh
*NOTE* I'm not saying they're useless exactly, just that as I've been around with my build and I've fought other with other spells (who claimed to carry so many games before, etc)And beat them within 4 seconds cause they couldn't escape, didn't have mana, not enough A.P., etc, etc. In the long run these spells are the only viable ones that help you enough.

Use your Lucent Singularity a lot! at higher lvls of A.P. you can one shot all of the minions up to the cannon minions. Never waste a snare on the minion if you don't have to, if Flash is on cd and you are getting beaten by something then use your slow first, if they catch up still then use the snare.

Items may seem a bit odd, Doran's Ring To start of with, good mana regen and some ap to boot! From there you build the almighty Ionian Boots of Lucidity, these awesome shoes add to your cd reduction, Amazing right? Yes, they are. The next item I focus is Rabadon's Deathcap, just a nice boost of ap straight off the back. Then I build a Rod of Ages Starting with Catalyst the Protector. From there you'll want to build a Zhonya's Hourglass Starting with the Needlessly Large Rod. After this you build up the Morello's Evil Tome, a very nice item giving you some cd reduction and a nice bit of mana regen as well as 75 AP. The last item I get is Rylai's Crystal Scepter, for the ap, health, and the slows.

Most people wouldn't know how to play her as an AP carry so ill go ahead and spell it out for ya! (just kidding I trust others should know a lot of this already :D) When playing Lux no matter what you do, DON'T INITIATE, that is the TANKS JOB NOT YOURS. Stand back when the tank engages in the fight throw down your Lucent Singularity first then pop up a nice Light Binding so they can't escape your wrath! If the fight doesn't exactly go your way pop a Prismatic Barrier on your team to delete some of that nasty damage. When ever you see the an enemy at low health that's when you use Finales Funkeln to finish the job. *IMPORTANT* Don't waste your ult all the time it may have a low cd but you never know when you might need it!

In Conclusion to this guide, I'd like to ask of anyone that uses it, not to rage at me when you don't carry a game. The Guide in itself is just a small instruction guide that is based on how well you execute your abilities and place yourself, please Remember that YOU are the carry, What happens will be determined by YOU and your TEAM. Well I hope you have fun and good luck with playing Lux!