This is my first build. Although it is a bit squishy I find it works for me. When you lane you want to use an ability, basic attack once, run, repeat. If you get in a good position and sneak up on someone you can usually gank them by casting q, attack, e, attack, r and that will usually kill all but the toughest champions.
Lux is very squishy, so don't push alone and when you do push, stay behind someone else. That way if things start to go badly, you can cast light binding to cover yourself and your teammates and get out of there. You can get out of most bad situations with a well cast light binding.
You can also harass enemy champions hugging a turret by casting lucent singularity, running out of range of the turret, then exploding it. This is a lot of fun to do early game. Another good thing about lucent singularity is that if you cast it in bushes you'll be able to see hidden enemies waiting to gank you, and you can gank them instead.
Once you're level 16 with this build you should be able to cast your ultimate every 30 seconds. I use it a lot both at the beginning and end of a team fight. It's also good to kill unsuspecting enemy champions at a distance. Or to quickly clear away some minions during a push. Late game, I find myself using Finales Funkln just as much if not more than any other ability.

The item build is designed to dish out a lot of damage in the shortest time possible. I always start with a [Meki Pendant and either two Health Potions or a Health Potion and Mana Potion. Lux is very squish so you'll probably want to carry around a Health Potion pretty far into mid game just in case. The next thing I do is get a Fiendish Codex to boost my mana regen and ap a little bit, then I go for Boots of Swiftness. Sorcerer's Shoes is also a good option if you'd rather have a little extra magic penetration instead of speed. Then I pick up Nashtor's Tooth for the attack speed and cooldown reduction. After that the rest of the items I go for the most AP I can get starting with Rabadon's Deathcap. Then I get Rylai's Crystal Scepter for the added health. Next I pick up Lich Bane for the increased mana and movement speed. And I finish it up with Hextech Gunblade.

For my skills I usually focus on light binding and lucent singularity early game. I usually wait until I have no other choice to get Prismatic Barrier because I find that when I'm getting ganked I die before I'm able to cast it. Really the only time I use it is during late game team fights to buff up my team.