If you want to be the best Arcane Green Lantern, this is how you build.  Grab your gum because it's Double Bubble time, and Arcane doesn't allow his allies, or himself, to fall in battle.

Amps:
Inverted Booster Gold (+10% all shields, not just to self)
Will Force 2 Eye of Ekron
Accelerated Abin Sur's Lantern - This can be swapped to any other mod to improve one of the other items if you are confident in your ability to not die.  I still like to use this because it gets you the maximum will regeneration/will in the shortest amount of time.  A good alternate choice may be upgraded Metallo's Heart


Skill order:
Ult -> Passive -> e -> w -> q

We're helping allies stay in lane through the passive that will be immensely improved by the build, and also increase your own sustainability.  The damage comes later because it's late game when you actually begin to build PD gear.


Build order:
Oa 2 first, wait until you can buy 1 will/hp potion (or you can skip if you are confident).
Lantern 2
Grodd 2
Oa 4
Qward 2
Grodd 4
EoE 4 or Booster Gold 3
Other of ^
Lantern 4
Qward 4/Metallo Heart max

This build order is to maximize the time you have investment 2 up.  If you have less than 2 PD champions on your team (not including you), you may find it more useful to sell the qward 2 and get the Metallo's heart instead.


Playstyle.

You can play pretty passive with this.  Whack the creeps, get hp back, and toss your lantern/construct for pokes.  Construct is best to prevent ganks on your lane partner, as the knockdown is very effective CC.

If you are being chased, its also good to throw  the lantern slightly behind you or slightly off your current path so that you can chain the enemies following while you escape.

One you have both Oa 4 and Grodd 4, you become a defensive god.  Watch which enemies are the most dangerous, and figure out which target they are going after, and grodd them immediately.  If your opponents have a deadly AoE ult (green lantern, for instance), that's the time you want to use Oa, or if you want to just improve your teams survivability during a retreat or chase. 

Your ult is your middle finger to the enemy when the enemy thinks they can finally get a kill while you aren't there, or if you are there and your shields are down.

Live for the bubble, never die in the bubble.  The bubbles are your friend, your ally, your partner.  Treat your bubbles well, and you'll never be alone again.