http://www.mobafire.com/league-of-legends/champion/gragas-45 My Favorite champion, and i think i have played him enought to share my thouths and expierence about him, So here i bring you his guide and his story ;)

The foothills of the Great Barrier are home to the hardiest people found anywhere on Valoran. Only those with great fortitude and endurance dwell in what is perhaps the most rugged and unforgiving environment anywhere on the face of Runeterra. It is here that the mighty Gragas keeps permanent residence, living south of Noxus. This behemoth of a man has long eschewed the rigors of civilization for what he calls his ''slice of paradise;'' he has no neighbors to bother him and plenty of space to pursue his life's ambition - brewing. Grogs, ales, meads, and wine - nothing is beyond his skill to brew. What makes Gragas a truly special brewmaster, however, is his proximity to a large and powerful nexus.

The magic of this nexus has seeped into his fermented creations, and Gragas has consumed enough of his own poison over the years to slake the thirst of an army. This arcane alcohol has caused Gragas to swell both in height and girth; he looms over the tallest of men and boasts nearly twice their width. To complement his immoderate size, Gragas has developed an ornery temper - one fueled by liquor and raw magic. His infrequent sojourns into Noxus for supplies always unfold the same way: Gragas enters a Noxian tavern, Gragas gets into several fights, Gragas lays out countless citizens, and finally Gragas flees for the foothills with Noxian constables in hot - though reluctant - pursuit. His misadventures have garnered him the attention of several summoners in the League of Legends, and he is now a willing champion in the arenas...doling out hard liquor and harder fists.

The Rabble Rouser leaves a path of drunken destruction in his wake, both in the Fields of Justice and off.

Summoner spells must be Flash-Ignite if you are in mid lane.Summoner spells can be Flash-exaust if you are up against a strong AD Champion in top lane, such as Renekton,Olaf.
never ever take teleport on gragas it is a useless skill for him cause he walk around wery quick anyways.
Clarity is a useless skill aswell, because he gains all the mana he needs from his w and blue buff.
Ghost is useless skill for gragas, because he is realy quick anyways and doesint need the speed from ghost to catch something.

I recommend taking offece tree for maximum damage posible, then the other 9 points to utility for DTR (death time reduction), more movement speed and the longer buff duration for longer blue buff is realy good, cause u can spam your skills for a litle longer before the blue runs out.

lvl 2 skill can be E if you see you need more damage early on,if you just want to farm more pick up W.This Skill Sequence is aimed at giving you the most damage posible.

Greater Glyph of Potency can be changed to Greater Glyph of Focus, if you think you lack Cooldown reduction, but i dont recomed you to do that, if u want to change glyphs better take m-resist.

I recomend taking lich bane after rabadons because it gives u much more bust damage when u come close with your E. Void staff is a must after lich bane, because most likely enemys will build m-resist due to your masive magic burst.
Zhonya's Hourglass and Will of Ancients can be picked up as you want, if you are quite fed and you want to come in closer to do much more burst, pick up the Zhonya's Hourglass, if you arent as fed and want to stay more in the back pick a Will of Ancients first.

Stacking dorans is a good idea because Dorans items stats are much higher then you should get for an item for this gold ammount.they give you AP, mana regen and HP for survivabillity that makes you much harder to kill early game.

Picking Rabandons for your first major item gives you lots of AP giving you huge burst at Mid game and giving u the cababillity to 1 combo more squishy Champions.In most cases you will be put up versus squishy AP champions in mid that will be killed wery quick and easy.

Lich Bane gives you the abillity to do magic damge with your next basic attack after a spellcast equal to the ammount of you abillity power. This almost works as another damage skill and gives you much more damage when atacking with you basic attacks and makes your burst totaly lethal to almost any champion that doesint have M-Resist.

Try to Farm up as much as posible at early game,because it is realy easy using your Q and E abilitys. That will give you a huge advantage, in mid and later game, cause of your burst being so hight you geting you dorans faster will make u win the lane easy. By the way when you farm minions with your Q ability try hiting your oponent as well, that will help out wery much.Pushing the lane with gragas is wery easy, that lowers the enemys CS but opens the enemy jungler to gank you much easyer.

Probably alot of you have seen that gragas has ruined your chase by throwing the enemy away or killed you with his ultimate by throwing the enemy right at you. The key is to watch the litle dot in the midle of the AOE skill range when the dot is behind the enemy the ultimate will throw the enemy at you if the dot is in front of the enemy it will throw the enemy away. when the enemy is moving the key is to aim the trajectory well.

Using the Q in the right way is easy. The best way is to try to hit your enemy with it when you use it to farm minions. try not use it to harras from far distances, cause its easy to dodge it because it has a rather slow moving speed.

Gragas is one of the most powerfull AP champions in League of Legends nowadays. his amazing utility damages and survivability makes him very strong in any lane.
Utility-E ability (Body Slam) makes Gragas dash forwar alitle (Can dash through walls to escape or catch enemys)+ the AOE(area of Effect)colision slow makes his E ability a wery strong Utility Spell.R abillity(explosive cask)an AOE nuke damaging and throwing around all enemys in the area (utilising with throwing your enemys around)More about his R(ultimate) in the section (How to not fail with your Ultimate)
Damage- Q-E-R (Q Barrel toss, E Body Slam, R Explosive Cask.)all these skills work realy well together, as i explained before.
Survivability- Passive-W-E-R (Passive-Happy Hour, W-Drunken Rage, E Body Slam, R Explosive Cask) W gives you a temporary buff that gives you damage reduction to all hits you suffer, increases your Attack Damage and restores some mana. E gives you the ability to escape wery easy, cause e dash works almost as a flash just a litle bit slower. R you can just push enemys away from you or your allies.His passive regenerates 2 % of you maximum hp over a short time, everytime you cast a spell.

Pros

-Wery good lane sustainance with his passive and W abbility.
-Can escape easy using his E ability every 4-6 sec. Depends on CDR.
-everysingle damage skill does AOE dmg meaning u can poke down enemys in a bunch.
-Absolutely Long ranges.
-Works good in all lanes.
-Amazing range makes his able to poke down enemys before team fight starts.
-Amazing AP Ratios on Q and R ability.
-Has great utility.
Cons

-Basic attacks are in meele range,meaning for bigger damage he needs to come close.
-Falls of later in the game.

This guide is not Finished yet . I am Trying to get fotage for the full guide, hope to bring the full guide as soon as posible.