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.

(http://leagueoflegends.wikia.com/wiki/Lux_the_Lady_of_Luminosity/Background)

Lux is a great champ, very over powered if played right. A lot of people I see play her, don't get many skill shots or miss the little things like auto attacking after landing a skill. She, in my eyes, is the best ap nuke in the game if you get that essential first stun off. Play her defensively until you are either over levelling your opponent or building faster. You will find that she is squishy and it might get annoying, but the healthy ap items just don't cut it for me. Once you get that Tome your ult will have a 24 second cooldown, SPAM IT use it to clear waves and nuking, GREAT for assists and kill steals ;)

Have fun.

With the build I have, you are going to be quite squishy. If you're mid play defensive get stuns off and make sure to auto attack after for your passive. Harass them down to about half health and keep them there so when you're level 6 you can nuke them. A lot of people buy rod of ages or arch angles, although they are good for sustainability lux needs pure ap to dominate opponents.

Your combo for nuking is very important, if you do not get a stun do not combo (unless team mates are available for extra damage). Lead with the stun as shown in picture, use your pool and ult all at once before the stun wears off. I normally stun, auto attack for passive, pool auto attack then ult, but you have to be good with skill shots (harder combo but possible with practise).

Although one them was a defeat I still only had 3 deaths, play lux defensively until you get the right opportunity and you can get kills all the time. The build is out of order I move stuff around during game so still try to stick to the order shown.

Lux benefits from cooldown reduction more than most champions, as her spells are on a longer cooldown than most caster champions. Try obtaining the Crest of the Ancient Golem buff (blue buff)to use Finales Funkeln (laser) as an effective poke ability. Cooldowns are a must hence the cooldown items I have in my build.

Clarity is a 'non-targeted' Summoner Spell. This spell instantly restores a portion of mana for yourself and half for all nearby allied champions.
Strategy
Clarity is best taken in teams where most, if not all, champions are mana based. Usually this spell is taken by a mana-hungry champion that needs to compensate with low base mana/mana regen (ie. Malphite), or focuses on aggressive play by spamming their skills (ie. lux). (http://leagueoflegends.wikia.com/wiki/Clarity)

I only use clarity because I spam my ability's to hell to harass the enemy champions, it is not essential but highly recommended.

You could also use other spells such as, teleport, ignite and possibly cleanse only because lux is squishy.

Lux's shield can be essential in some cases, for example if your team mate is ignited your shield most of the time can save them from death. If I mid as lux I don't get prismatic barrier until it forces me too, I play lux very defensively and will not need this until the laneing phase is over.

FARMING IS ESSENTIAL.

Farming lux will give you a great advantage over the other champions. At around 10 minutes through you should have enough ability power from the farming you did too one shot caster minions with Lucent singularity (pool), thus making the gold go up and up.

(Image has no credit towards me)
Make sure you try to hit all the minions at once so that you can auto attack them after for more effective minion kills.