Born to the prestigious Crownguards, the paragon family of Demacian service, Luxanna was destined for greatness. She grew up as the family's only daughter, and she immediately took to the advanced education and lavish parties required of families as high profile as the Crownguards. As Lux matured, it became clear that she was extraordinarily gifted. She could play tricks that made people believe they had seen things that did not actually exist. She could also hide in plain sight. Somehow, she was able to reverse engineer arcane magical spells after seeing them cast only once. She was hailed as a prodigy, drawing the affections of the Demacian government, military, and citizens alike.

As one of the youngest women to be tested by the College of Magic, she was discovered to possess a unique command over the powers of light. The young Lux viewed this as a great gift, something for her to embrace and use in the name of good. Realizing her unique skills, the Demacian military recruited and trained her in covert operations. She quickly became renowned for her daring achievements; the most dangerous of which found her deep in the chambers of the Noxian High Command. She extracted valuable inside information about the Noxus-Ionian conflict, earning her great favor with Demacians and Ionians alike. However, reconnaissance and surveillance was not for her. A light of her people, Lux's true calling was the League of Legends, where she could follow in her brother's footsteps and unleash her gifts as an inspiration for all of Demacia.

''Her guiding light makes enemies weary, but they should worry most when the light fades.''
-- Garen, The Might of Demacia

Illumination
Lux's damaging spells charge the target with energy for 6 seconds. Lux's next attack ignites the energy, dealing 20-190 (depending on Lux's level) magic damage to the target.

Pretty freaking awesome passive. For farming, after a couple of levels in Lucent Singularity,you just need one autoattack to kill caster minions. For harassment vs champions, just throw a Lucent Singularity and autoattack them, after a while they'll start playing defensive. For a offensive combo, use your Light Binding, autoattack, Lucent Singularity, autoattack.

Light Binding
Fires a ball of light towards a target location, binding and damaging up to 2 enemy units. The first target takes 60/110/160/210/260 (+0.7 per Ability Power) magic damage and is bound for 2 seconds. The second target receives 50% of the effect.

This skill is pretty freaking awesome, 2 second bind at level one, and since we only use it for the bind, we level this last. Since it's your best defensive mechanism, NEVER use it to last hit creep until you get close to max CDR and you're sure that there is ABSOLUTELY no possibility of being ganked. Always aim your light bindings as a miss or hit decides whether you/your teammates survive a chase/gank, and whether you kill the enemies or not. It's always better throw the binding later and hit someone, than just throw it out of panic and getting yourself killed. It's hilarious when you shackle Rammus right in front of your tower when they try to dive you.

Prismatic Barrier
Lux throws her wand to the target location and back, protecting herself and all allied champions it touches from 50/75/100/125/150 (+0.35 per Ability Power) damage for 3 seconds.

Not much explanation needed, throw this toward your allies when they're getting hit, and use it when you're getting hit, note that the damage prevention is in 2 packets, so don't expect to survive burst damage with this. This comes back to where you currently are, so if you miss your first throw, make sure you catch your allies with your return swing.

Lucent Singularity
Creates a zone that slows enemy units by 36% (zone lasts 5 seconds). Can be detonated to damage enemies in the area for 240 (+0.6 per Ability Power) magic damage.

Use this to farm creep, slow creep pushes, throw this and wait until the majority of the creep are in it, then pop it to slow minion pushes towards a defenseless tower. I don't really recommend checking bushes with it since you already carry CV, but it's not too bad if you do. Standard harassment if hitting them with light binding is not possible is a Lucent Singularity followed by autoattacks.

Finales Funkeln
After a short delay, Lux fires a stream of light in front of her, dealing 300/400/500 (+0.85 per Ability Power) to all enemy units in the area.

Took me a while to get used to it after playing Ezreal, but it's pretty simple after a while, just aim a little bit ahead and they'll walk right into it. I mainly use it to finish people off, and to grab buffs. When ganking, you want to throw your Lucent Singularity first for the slow, pop it and autoattack if you're within attacking range, if not, keep it on, throw your Light Binding, pop your Lucent Singularity and Ulti the poor dude who got bound. Note that your ulti also pops your passive, so if you ulti someone with health around your ultimate damage, and they have your passive on, it's almost a guaranteed kill. Most people underestimate Lux's ulti damage, so you gotta teach them a lesson.

Update
After a while, I found that the best Lux build is simply the one that goes pure damage, since all your spells are long ranged, you don't even have to be in the teamfight and you should take no damage, I changed my playstyle to a long range caster and saved my ulti to finish off people and suddenly, I'm doing a lot better. This build focuses simply on AP and CDR and no mana regen because that would delay your damage, I almost never never never go glass cannon on ANYONE, but for Lux, its the only viable build.

Reasoning behind Summoner Skills
Instead of grabbing both Ghost and Flash, I chose Clairvoyance and Ghost because instead of having to Flash away from a gank, why not just walk away before they even get into position? My philosophy is, there's really no need for 2 escape summoner skills if you don't get into the position where you're being ganked in the first place. A lot of people underestimate vision and what it can do. Clairvoyance can save your teammates from ganks, win the game with a steal on Baron, see sneaky jerks trying to steal your buffs, see the lane compositions in the beginning of the game.
Flash
Not that useful on Lux, as all her skills are very long ranged, can finish people off with Ulti(mind you, I'm the guy that gets Flash on EVERYONE), I find Ghost to be a better skill to run away from 5 man ganks as those are the only ones that are capable of chasing Lux.
Ignite
No, Lux is a long range champ, if you're going in to Ignite someone, chances are that you're dead already, especially with the AP Carry build. I play Lux as more of a "Marksman/Sharpshooter" probably because I'm raging at Caitlyn for being useless as a sniper(bought and refunded her).
Clarity
Please, no. It works on Blitz, but not on Lux, if you're having mana troubles, just go grab Mana Potion or a Chalice of Harmony FFS, but NEVER CLARITY.
Clairvoyance
PLEASE USE IT EVERTIME IT'S OFF COOLDOWN, JUST DO IT, K THANKS. Clairvoyance spots should be same as the common ward spots, go find the chart somewhere else. Having this also makes you look pro.

This build looks kind of your standard "PEW PEW KILL EVERYONE" build and you might say WTF? , but that would get you killed in every single teamfight. Luckily, Lux is actually one of those characters that never have to get close to people to kill them. Remember, you're the AP carry, the person who nukes the entire enemy team and instagib squishies. If you've played Lux before, you will find out that NONE of her skills require her to be in the actual teamfight, all she has to do is skirt around the edges, throw spells in, shield teammates being focused, and ulti whoever is running away, or will run away if you don't ulti. If you ever find yourself being focused in a teamfight, you're doing something wrong, and should examine your Lux playstyle. Lux is like a marksman, and marksmen should never been in the actual battle.

With all the stress being put on not being in the actual teamfight, it's really up to the player. With more skill, you will know how much punishment your champion can take before dying and can serve as awesome bait. For new Lux players, the advice in this guide should be followed before experimenting with various styles of gameplay.
Build
1. Doran's Ring
The AP build start off with a Doran's Ring because of the amazing stats that this simple item gives, sometimes instead of getting a defensive item, stacking 2 or 3 of them works wonderfully.
2. Mejai's Soulstealer
This build then goes straight to Mejai's to start your WTF Lazer Pew Pewing.
3. Ionian Boots of Lucidity for CDR
6. Rabadon's Deathcap
After that, build Rabadon's Deathcap for more AP.

No mana regen items, so ALWAYS get blue buff, no matter how you get it, just do it, whether you have to ks your teammates. Also keep a couple of mana pots just in case.

If you suck at Lux and you're missing your skillshots, just remember, patience goes a long way, waiting that extra half a second to aim your skillshot pays off a lot more than a random skillshot that hits nothing. Besides, it looks really bad if you miss your Bindings or your ultis. I raged at myself last game for missing one ulti that could have been a double kill(well actually, I shot it right in between them, so it would have been only one kill had I hit someone).

You're the AP carry. You should get mid or solo top lane. With that being said, either it's you versus 2 people, or one if there is a jungler on the enemy team. Your job is to stay alive. It's not to kill the enemy player, it's not to deny the enemy, it's to stay alive. It's great when you can do those 2 things while staying alive, but the priority is still surviving. Dying in a solo lane is really really really really bad as the other player gets gold, exp, and gets freefarm while you're looking at the respawn timer and wasting the exp and gold that the solo lane gives. Dying in a duo lane is fine, someone is there to grab the exp and gold, but not in a solo lane.

Moving on, play passively, last hit minions, never use your Light Binding unless it's to defend yourself or when your jungler ganks. Lucent Singularity, however is a whole another story, use it to harass the enemy and throw in a couple of autoattacks in if possible without taking too much damage. Most of the damage in the laning phase will come from autoattacks, so DON'T NEGLECT AUTOATTACKING!. I hate it when I see people not autoattack because they're a caster. If you are within range, do not have 50 billion enemy ranged minions right next to you, will not get punished for attacking, DO IT. Laning should be pretty easy as you can cope with heavy lane pushing, stop ganks with Light Binding, shield skillshots with Prismatic Barrier(only when it's necessary), and have CV to check on players around the map and also to annoy players trying to leech exp in a bush. If you ever get below 1/4 health, please just go back, maybe people aren't tower diving you now, but if you have 50 hp, I WILL DIVE YOU, and I will not be deterred by a single tower hit. Be generous with health pots, mana pots only if you're jungler is a ****** and won't give you blue buff. After laning phase.....I basically described your role in the rest of the guide.