Hello, and welcome. Arcane Green Lantern is a remarkably versatile champion. He's an extremely mobile tank, with the ability to turn the tides of games with his strong CC and fight-deciding ultimate. This is how I build him, and use him, as a support bot lane on Coast City.
First, start the game with his Q and a level 2 Olympus Gambit, and level 2 Health Vial. This way, you start with the maximum possible farm from your lane via the Investment keyword, and have a bit of extra sustain. If your team does the initial invade, set a cam to see a reverse invade coming (either on your "big camp" or in the stealth pad just below it... I usually drop it in the corner of that pad) and head to the stealth pad above the DDD pit. If they're already advancing on your stealth pad, that's perfect; use your Q to knock them down and fall back a bit, letting those with ranged attacks do their damage, but try to be between the rest of your team and the enemy, especially if you have no other tanks on your team. If they are invading hard, it's almost always good to drop down a healing wave if you're in the proper position. If your team is trying to invade, rather than their team, use your Q for its knockdown power again, hopefully knocking down a squishy who's too far forward if you're lucky. Anyway, after the initial teamfight, it's time to head to lane.
ArcGL is mostly about peel, in lane. If they're pushing you in hard, make sure to keep applying your passive for additional sustain. If you find yourself consistently pushed in, it might be smart to level your passive earlier than in this guide's suggested above... the suggested leveling order is for either fighting evenly in the middle, or pushing them into tower.
When being pushed into tower, your main concern is keeping your carry able to farm under it. Don't spend your skills for waveclear much; this build is intentionally low on will, so skill-spamming is a bad idea, esp. when pushed under tower. Use Q when they come in hard to knock someone down, preferably the carry so yours can get some free autos down. If they're coming in really deep, use your W and E, throwing the lantern towards them if they run back towards their turret, otherwise just holding the chains on them with the W. ArcGL lanes don't often stay pushed into tower long, but it can happen if the support is something with good waveclear and the enemy pushes hard. If it does stay pushed, your jungler(s) should be able to punish them extremely easily, with your help.
In an even lane, or one where you're a little pushed but not under your tower, try not to push too hard into them if you can avoid it. Let them push a little... then it's time for the combo. Q the carry, use the second activation to jump right on top of them, press W. Throw the lantern if they back off and are still chained. If your carry understands how that works, it makes for extremely good trading, and is worth the will expenditure.
If they're playing under their tower, but far forward under it, use your Q to harass, esp. if your carry is good. Hopefully, when you hit it, they can get a few autos down. Don't spam it, but it's the best way to get free damage on them if you're dominating. If it's a little later and you're dominating hard enough to want to dive, ArcGL dives extremely well, using the same combo I described above. As long as your carry joins you to apply damage, it can be a nice "win more" if you're ahead, or if they're just low under tower.
When playing ArcGL, a good bit of map awareness is required, to best use your ultimate. If the enemy jungler is in your jungle and engages on yours, ult your jungler and turn the fight, using again the basic combo I described above. There are times when this isn't the most optimal, but it's often a VERY good use of your ulti. It also allows him to only have to walk halfway up for that top relay fight, meaning he can stay and hold lane until about 20 seconds before you expect the fight to happen, ulting in when the enemy engages onto one of your carries.
As for building, you're pretty much building a tank. You want Atlantean Royal Seal immediately after your starting items, and you probably want to just straight max it first. After that, it all depends on what sort of damage you're taking, and how aggressive you want to be. The items I put into Offensive Items are the items you take if you want to be highly aggressive; the defensive items are the items that you take most games. Pick the balance that works best for the damage you are taking. Your main objective is to be as tanky as possible, against your lane before about level 10 (including the jungler you see most often if they're in lane a lot), then against the entire team comp after that.
Building more damage on ArcGL is generally counterproductive. You want to be the one who jumps right into the enemy team, and uses that CC combo to slow, lock down, and knock down as many as possible. In dire straits, you can escape better than any other tank if you do it right: First, use Q, over a wall if you can. Then, drop your E right at your feet, and hit W when the ones chasing you are in range. Late game, this makes you able to exit nearly any fight at will, if your skills are up. Using your ulti to escape isn't usually a great idea... it takes a fair bit of time for you to teleport to where you are trying to go, and the rest of your kit is far better at doing that.
Well, best of luck, Protectors. I hope to see you in the Trials!
Isn't him a mana hungry? 
where the FUCK is the 'guide'? 