Welcome to my first guide! Lux is a quite a powerful champion that many people ignore in League of Legends. This guide is an AP build on Lux. So please enjoy this guide and hope you will learn something about Lux. Feel free to post comments that will help me improve this guide along with some other feedback. As I always think: No one is perfect and there is always room to improve.

-Lux
-Some skill shots
-Might have to solo lane
-Gank properly
-Press buttons very quickly
-Last hit creeps (Maxamize gold)
-Enjoy using Lux

Pros:
-VERY powerful late game
-Great ganker
-Can spam enemy champions
-Can check for ganks
-Dominant in lane

Cons:
-Squishy
-Can run out of mana early game
-Not great escaper
-Can die easily if focused on

Masteries:
I always go with 9/0/21 because it works best for AP Lux. Cooldowns and mana regeneration are very important for Lux because she needs as much mana as she can get early game.

Summoner Spells:
I usually get Teleport, Flash, or Ghost.
Teleport Teleport will let you stay in your lane as much as possible to maxamize your exp. Ghost will let you run away from enemies chasing you. Flash can help you escape ganks.

What You Should Consider Getting:
Ghost Ghost will help a lot because she is not a great escaper. Her only hope is Light Binding and that won't help too much when you're in big trouble.
Flash Flash may help you escape, but you could still be chased down if there's someone such as Kassadin.
Teleport will allow you to stay in your lane as long as possible to maxamize your XP intake.
Exhaust Exhaust is not very useful for Lux. Only used to slow the enemy chasing you or "maybe" get first blood.
Cleanse Cleanse will only get you out of stuns and etc. It can help you escape ganks if someone such as Sion stuns you.
Ignite Ignite will give additional damage to MAYBE get first blood.


Runes:
Greater Mark of Magic Penetration This will give some great magic damage early game.
Greater Seal of Scaling Mana Regeneration Remember, the more mana, the better.
Greater Glyph of Scaling Ability Power Even more magic damage early game!
Greater Quintessence of Health Lux needs as much HP as she can get in early game. She is very easily killed early game if you don't play her smart enough.
Greater Quintessence of Ability Power This will give Lux MORE magic damage!

Illumination- This passive will give you some great damage early game.
Light Binding- When executed correctly, your team can pick up a kill by trapping the enemy champion. This can help you escape, but it will not help when facing someone such as Master Yi or Kassadin.
Prismatic Barrier- This skill will allow you to gain that extra bit of hp. Always use this in team fights. This skill saves lives and is very useful.
Lucent Singularity- There are some helpful uses for this skill. One use is to check brushes to see if there are any upcoming ganks. It also slows enemies who are in the barrier. The great thing about Lucent Singularity is that you can choose when to activate this skill.
finales funkeln- This ultimate skill is very powerful, has a long range, and has a short cooldown. Use this skill frequently. This skill and do over 1.5k damage at end game!!!
-Take away their HP when they are all together before the team fights begin.
-Kill someone when they think they are safe behind their turret!
-Make them run in terror when they have barely any HP left!
-Use it as part of your combo!!!

People usually think that they need to save up their ultimate for the "perfect" moment. Lux can break this rule. Since her cooldown is only less than 40 seconds, you can use it whenever you want. If you really put everything on cooldowns, then you can get it to a minimum of 24 seconds! The only real problem with Lux's ult is that it requires some skill shot. If you miss, then the good thing is that you only have to wait for seconds.
There are only two possible ways that Lux uses her ult at the wrong time:
-You accidentally clicked it and you really wanted to use it on something or someone 5 seconds later.
-You use it and an UNEXPECTED event happens.

So remember, use Lux's ult frequently! Don't be scared to wait for the "perfect" moment!

Try to always last hit minions early game to maintain maximum gold. Your Lucent Singularity can destroy whole groups of minions late game, which will give you tons of gold. If you are going to push a lane, just keep using Lucent Singularity to destroy groups of creeps.
Once your level is high enough, you can go jungling with the following combo:
First, use Lucent Singularity, but don't activate it.
Second, use Prismatic Barrier to portect yourself from damage so you can receive as little damage as possible.
Third, use Light Binding to trap them and then quickly activate Lucent Singularity.
Then, your Illumination passive will most likely finish them off.

If you are playing as Lux and you are not soloing, then this will be a great advantage for you guys. Just keep harassing the other teammates with Lucent Singularity. If you have a partner with a stun such as Taric, then you two will dominate the lane! If you two find yourselves defending your turret, that's ok! When they push too far, they have to be careful of ganks.

1v2
If you have to solo against two other champions, then ALWAYS defend. Never push when you are soloing a lane. If you push, then it will be very hard to run away when you get ganked or if they start to attack you. While defending, just use your Lucent Singularity to kill the creeps next to your turret. If they are attacking your turret, use Light Binding to trap them and maybe the turret will attack them. If you defend, you win. If you push, you lose.

1v1
If you are going mid, then always buy some health potions. You want to stay in your lane for as long as you can. Why?
-Your turret might get damaged
-The enemy will gain more xp than you do
-To maxamize your gold
If you are going to push mid, then make sure you check for ganks in the brush with Lucent Singularity once in a while. If defending, just harass them with Lucent Singularity, which will get them to not attack the turret.

First get a Doran's Ring OR a Boots and 3 Health Potion.
Once you have enough gold, go back to base and rush a Mejai's Soulstealer along with more Health Potion.
After that, get your Sorcerer's Shoes. Why not Ionian Boots of Lucidity? Because you already have masteries to help you with your cooldowns.
Rabadon's Deathcap is expensive so you may have to go back to base 2 or 3 times to get it. Get the Needlessly Large Rod first then the Blasting Wand.
A Banshee's Veil is a must because Lux is a squishy champion and if she gets stuned, she is screwed. This item will help her a lot.
Sell your Doran's Ring now.

You can only fit in two more items now and it totally up to your own decision.
Lich Bane will give great ability power, mana, and magic resistance. Your auto attack will also do tons of damage.
A lot of enemies have quite some magic resist so the Void Staff should give you that extra BAM!
Zhonya's Hourglass will save your life if you are being focused!
Archangel's Staff will give you a lot of mana and AP. Your ult will do over 1k damage!

When you are wandering around the map and you find yourself with another enemy champion, then this is what you should do:
First, use Light Binding so they can't move.
Second, use Lucent Singularity but don't activate it.
Third, use finales funkeln to take away a whole lot of HP.
Fourth, activate the Lucent Singularity.

It should go like this:
Light Binding -> Lucent Singularity -> finales funkeln -> Lucent Singularity

You have to do this fast, or else they might escape.
After this combo, they should be dead, or they should be running away.

NOTE: There can also be a fifth step, which is to use your auto attack on them after you activate Lucent Singularity to do further damage.

When you find your team in a team fight, always help them!
Use your Prismatic Barrier to protect your allies from damage.
Trap the enemy champions with Light Binding that are trying to run away.
You can use Lucent Singularity to slow the enemy champions.
Remember, finales funkeln has one of the shortest cooldowns in the whole game. You can use it in the beginning of a team fight, and if the fight goes long enough, you can use it again!
When you find yourself being targeted, NEVER travel along. Travel with your team and ALWAYS check for ganks with Lucent Singularity.

Levels 1-6:
I always get Lucent Singularity for my first ability. I don't get Light Binding first because it really is useless. Lucent Singularity can also be used to check brushes to see if the enemy champions are there. In a minute after the minions spawn, you will be level two! Then you get Light Binding. Lux can die very easily in the beginning, so be careful with her. You can start harassing enemy champions with Lucent Singularity, because it has a long range. Don't use it every time the cooldown is done, otherwise you will run out of mana. So time yourself. It is good to have at least 1 level of Light Binding just in case you are getting ganked.

Levels 7-13:
This is when Lux starts to get powerful. This is when people have to start watching out for Lux. You now have two options: Stay in lane OR help someone else (gank). If you decide to stay in your lane, I recommend NOT to push all the way to the enemy turret because the enemy might start ganking also. If you decide to gank or help a teammate, make sure there is someone defending the turret in the lane you left.
-NEVER leave a turret undefended because that is one main reason so many people loose games in LOL.
To gank properly, you have to wait for the perfect moment. Let the enemy push a little bit so when you gank them, they will have to run all the way back to their turret. I usually would use Light Binding to trap them first and have my teammates finish them off.
If a team fight does break out in mid game, then please refer to the section above this one.

Levels 14-18:
This is when Lux becomes very powerful. finales funkeln should now do TONS of damage and you killer combo will have everyone running in fear! Your Mejai's Soulstealer should have a high stack by now. Stay near your team during late game because Lux can still be killed easily when she gets ganked. If the enemy team has a tank that really starts to have a huge load of HP, use finales funkeln. Again, it has a very short cooldown so you can use it frequently! Your team should be going for baron soon and if your team finds the enemy team there, this is when you will shine. Your Lucent Singularity will hit them all and deal tons of damage because they are all so close together.

To summarize what you just read, Lux is a great champion to use and also a great support. She has great range and very fun to use. Remember, her ult is very powerful and has a short cooldown that she is one of the few champions that don't have to wait for the "perfect" moment to use it.
I do hope you have considered this guide to really help people who are struggling to use Lux and to encourage people just to try out Lux. Hey, if you try her out and you don't like her, that is fine with me. I hope you have learned something from this guide that doesn't have to be about Lux, but about the game as well.