The skills I recommend are Teleport and Clarity. Using these will allow you to be anywhere you need to be and endlessly spam your skills. The way I play Lux is pretty much using whatever I can whenever I can. The way you have to think about it is that if you think you can hit them with a Q or an E, then you probably can and to use your abilities accordingly.

For Masteries I take a standard 9/0/21 caster build. Making sure to get the cooldown reduction in both utility and offense trees the rest is mostly preference but I would suggest getting all the mana regen masteries you can aswell because you can never have enough.

This part is very simple, you can start with either Light Binding or Lucent Singularity depending on what you think will be most helpful for farming or harrassing. After that your main priority is [Light Binding] alternated with Lucent Singularity and taking Finales Funkeln whenever possible. The reason for not leveling up Prismatic Barrier is because of how poor the shield really is, the only useful situation for it would be if you could hit your entire team with it and that is unlikely.

Marks
Greater Mark of Magic Penetration
The obvious choice of any caster, magic penetration is one of the most useful stats in the game for any AP carry.

Seals
Greater Seal of Scaling Mana Regeneration
Mana regen PER LEVEL, early game stats are terrible because any balanced game should be lasting at least 40 minutes.

Glyphs
Greater Glyph of Scaling Cooldown Reduction
Again, early game stats are very weak and unnecessary .With these, your CDR masteries and [Morello's Evil Tome] will be around 38% CDR which can easily be topped off with Blue Buff, Elixer of Brilliance, or another CDR item that you might prefer over one that I use.

Quintessences
Greater Quintessence of Ability Power
These are the only early game runes i recommend because they give you a very good lead on AP when combined with [Doran's Ring] and they with compensate for the lack of AP until a bit later in the build.

Here are a few tricks I use when playing Lux.

Just like any other character with skill shots your not going to get very many off before you enemy learn to dodge/avoid your harrasment. The easiest way to get passed this is to just aim your Lucent Singularity slightly behind your enemy because when they see you cast their first thought is to back up.

Once you're able to land this almost every time, try delaying the explosion until you have an auto attack on the way to your target. If you do this you make then enemy think that they will be able to get out scratch free when all of a sudden the circle pops and your auto attack is already on-route so the damage is unavoidable.

Another extremely useful use for Lucent Singularity, is to use its ability to clear the fog of war by throwing it in bushes or popular ganking locations. This will give you a heads up on enemy positioning and can determine whether or not its safe to push that tower.

The only advice i can give for Light Binding is to try and lead your target like any other skill shot. When you're chasing an enemy, and is clear as day that you're trying to set up a snare, try to delay casting until your victim has attempted to juke you or slow them with Lucent Singularity and catch them by surprise.

This last tip is EXTREMELY VALUABLE, read carefully.
DON'T BE AFRAID TO LAZOR. With the amount of CDR you should have, you will rarely find yourself needing it again before its short cooldown. Of course take this statement lightly early game when you're still beafing up, but its always better to be saying "Meh, at least I tried," than "I bet I could've got 'em."