So, I'm just going to start with saying, I'm Rage, a casual LoL player and this is my first build to be published. I decided to start with Lux, because she's one of the champions I prefer to play and I have no problem for writing a guide for her.

So let's get started. Lux is considered a support but she fits much nicer under the mage or caster DPS category for the large amount of damage she can do around mid-late game. Her ult can do a large amount of damage doing over 1000 damage end game with a cooldown of only 24~ seconds and at a decently large range.

This is not to say she is not a support either though. Lux is able to snare AND slow multiple enemies at once, as well as shield her teammates from damage.

Greater Mark of Insight
Greater Seal of Potency
Greater Glyph of Potency
Greater Quintessence of Potency
The reason I've chosen these runes is because the extra AP is very helpful early game especially in team fights and ganks. As well having some magic penetration is always a great thing for a caster to have, regardless of the caster champion.

Although these runes do work well on Lux, there are many other setups you could go with such as CDR (cooldown reduction) or more magic penetration. It's completely up to your personally play style.
CDR Runes:
MP Runes:

The masteries I have chosen for my Lux build is a pretty common or is very similar to many other mage/caster champion builds. Many caster's are able to use a similar if not the same mastery setup and use it well.

You can play around with the setup but I find the above works well for most people.

You can choose many items that will work well on Lux but I believe my setup balances out very well between AP, mana, and CDR, which happens to work out very nicely on Lux regardless of your play style.

You could go in a very different direction of mind from my build but my build should work well for most.

You could use almost any summoner spell on Lux and do fine with them but I like to use Flash and Clarity.

This is because since Lux is fairly squishy she is targeted first a lot of the time so flash is a great way to escape from death or even get a kill depending on which way its going.

And the reason to why I use Clarity is because many times I'll be low on mana while fighting since Lux has low cooldowns with CDR and I can just spam enemies. It's always good to be able to fill your mana back up and continue supporting your teammates in a battle.

Some other options: Teleport & Fortify

Pros:

Able to play as a mage or a support
Good at farming
Has a slow & snare
Can shield self/teammates
Can get very low cooldowns

Cons:

Squishy/Normally targeted first
Can run out of mana fast (usually only early game)

Lux is a great team player champion due to her having a snare, shield AND slow. That's 3 of her spells that can benefit your whole team, as well your ult can be used to get run away enemies.

When I play Lux I am able to keep my team mates alive most of the time because I'll shield them and then snare my enemies giving my teammate a chance to get away without dying.

Farming and last hitting is very easy to do on Lux because of her e. She can easily kill multiple minions at once with it and almost always get the last hit making getting money and xp easy.

Lux with this build will work great on any ranked game because it can be used to not only do some good damage to your enemies but you can also keep your teammates from feeding.

You can shield them, then snare and slow your enemies.

If your teammates still manages to die after that, then it's time to find a new team!

Finally, Lux is a great champion after mastered and can do some serious damage and save your teammates ***'s at the same time.

I hope you like my guild and don't forget to rate!