Hello.This is my Luxanna Crownguard build.She can be amazing.She can be ure BFF.But she is my main and ill show you how to own with her,because she can be a good burster.
Because Lux sometimes if all about positioning and timing with spells.
BTW:If you wanna down/up rate this.PLEASE.Try it first.And if you see if i written something or shown something wrong type it in the comment's (but first read and see all of the build)

PRO'S
-dealing big AP dmg
-pinning down squishy target's
-surviving in team fight's
-getting kills/supports even if ure not in a team fight
-beeing a viable support at early game
-can steal dragon/baron

CON'S
-sqiushy early and mid game
-focused in team fight's
-dealing low dmg to stackers on MR

USABLE
Greater Mark of Magic Penetration-Since Lux has got a poor magic pen this should do the trick and help her pierce enemy's with big magic resist
Greater Seal of Scaling Mana Regeneration-Since Doran's Ring is your first item you will still need some mana regen and these runes will do the trick.Trust me you will need these.
Greater Glyph of Scaling Mana Regeneration-Just like Greater Seal of Scaling Mana Regeneration you will have even more mana regen.So at early game if u run out of mana,you wont have to Recall to base.You can just wait for your mana.
Greater Quintessence of Ability Power-While we covered the basic problem's (mana regen and spell pen) we will got 1 issue.Ability Power.Thats why there runes will give you some nice AP at begining that will help you threw all out of the game.
OPTIONAL
Greater Mark of Ability Power-These runes are viable if you dont want any magic penatration and you want only to stack more and more AP
Greater Quintessence of Scaling Ability Power-You can take these runes if u want more AP and if u are patient,because u need level 18 to get max AP from these runes.

These masteries are standard 9/0/21 for an AP/DMG

-The good old Doran's.This item will help you at early game because Lux has got poor HP.And the mana regen and AP from Doran's ring is always used.
-This item is most of the time useable/viable for Lux.Sometimes Lux has got good dmg and ally's to help her she can stack the Mejai's Soulstealer preety good.If she is not having a good game you can try to be a supporter then later on while you stack the Mejai's Soulstealer you can increase your damage and become an AP/damage again.Plus if u got 20 stacks you get some nice CDR
-The next item you need is the Rabadon's.All the AP/damager's buy this item.As threw out the game if you got good stack's on Mejai's Soulstealer you can get alot of AP out of this item.
This item should be gotten in mid gmae.Atleast at the end of mid game.RoA gives good HP/MP/AP that Lux use's.Nuff' said.
-The more spells you spam the better.With Archangel's you will get ton's of mana and mana regen.Plus of all IT GIVES AP DEPENDING ON YOUR MAXIMUM MANA. So the item's Rod of Ages and Lich Bane are in a combo with this item.
-This item is the last and should be gotten at late game.It gives magic resist,AP,mana and MOVMENT SPEED.With the combo of all of the AP items and the passive of Lich Bane, Lux with 1 hit (plus her passive)can deal about 600 and more dmg.

USEABLE
-These boots are one of the main boots for Lux.They give nice magic penatration.With the combonation of the runes Lux can pierce alot of magic resistance.
-These are the second main boots for Lux.They give lots of CDR wich affect's all her spells and make her spell's faster to cast.
OPTINAL
-These boots dont give CDR of magic pen but they give some nice speed.They are usefull for running faster to the base,out of the base,in and out of team fight's and escape purpous's.
-These boots are similar to Boots of Swiftness.When you get into a fight you lose alot of speed.The only thing these boots are usefull for is when u are ss/mia and u want to get faster to a team fight,base or a lane.
-These are the last optinal boots for Lux.If your enemy team has lot of CC.Then these boots are definetly for you.Because Lux can be easly pinned down with CC on her.

This skill sequence for some people may seem weak.But trust me.It is not.

-This skill sends out a nuke (light ball) that deals damage and binds the enemy target it hits.If the target is hitted the light ball goes further and can hit another unit for 50% of the damage and bind.This spell is very good because it is a CC and deals tons of dmg.Light Binding can be used to save ally's or catch up to enemy target's insuring kills or helping the team.In team fights its usefull to only hit 2 target's.(should be used on the strongest targets if u are retreating if not then on the weakest target's)
-This spell is a boomerang shield.When you throw the boomerang,it comes back.And shields double the damage.If positioned greatly you can win hard team fight's and escape sticky situation's.
-This spell is a AOE damaging spell.It sends out a bouble that explode's in 5 sec(you can activated it again to set it to explode earlyer).When you throw this spell into the fog of war you get vision around that spell.It can be used to scout for ganks and dragon/baron.It deals pretty strong damage and while the bouble is active it slows enemy's that go threw it.
Finales Funkeln-This spell is Lux's ultimate.It send's out a rainbow laser.It has a big range and deals ton's of damage.If positioned correctly you can kill enemy's from a big distaned about to recall.Imagine you got a enemy Vayne about to recall and you cant catch her,but you got your ultimate ready and you are in range of her to kill her.That is one fun way of useing Finales Funkeln.But in team fight's there is a combo you can use with Finales Funkeln just throw Lux's 3rd spell and make sure it hits all enemy target's and then use Finales Funkeln to hit most of the target's.(at level 18 with this combo you can deal about 1000 and more damage to units that didnt stack magic resistance)

-This is almost a must-have for Lux.You can use to catch enemy's and escape from death.
-This is a must-have for Lux,because it is almost like Ghost,but better.You can make distance from your enemy's,catch your enemy's,jump over walls to save yourself or an ally,flash over a wall to catch an enemy,.......
-Alot of people take Clarity for Lux.And i agree that Clarity and Lux are a good combo.Even if u got lots of mana,some of your ally's will need mana.And with Clarity you arent just a benefit for yourself,but a benefit for the ENTIRE TEAM.
-This isnt a summoner spell that Lux needs.But some player's use this.
-This summoner spell isnt used moste of the time,but it is usefull sometimes and its 100% usefull for a support Lux
-Not that much viable in game.
-Teleport is very viable.It can be used to protect a lane or escape ganks,even make a gank(when u teleport to a ward).Can be used by a Lux.
-Not useable
-NEVER!!!!!!!!
-Only useable if enemy got lots of CC and u dont wanna buy Mercury's Treads
-Preety bad choice for a summoner spell
-Only used by a jungleing Lux

These are some of the combo's you use for 1v1:
Combo 1:Q+basic attack+E+basic attack+ulti+basic attack
Combo 2:Q+Ulti+basic attack+E+basic attack
Combo 3:E+basic attack+Q+Ulti+basic attack

-If your enemy's got really high AD champ's instead of Lich Bane you can buy Guardian Angel, Thornmail or Randuin's Omen
-If your enemy's got really high AP champ's instead of Lich Bane you can buy Force of Nature, Guardian Angel, Banshee's Veil or Quicksilver Sash
-If the enemy has got a fed Veigar dont buy Archangel's Staff buy instead Banshee's Veil or Quicksilver Sash or Abyssal Mask.

Remember...
This guide isnt that difficult...You can try it out....Its fun
There are lots of guides for Lux but mine is really special to me.
and enjoy playing ! :D