dah hello my friends. this is an ad/ap/hybrid/tank/offtank/support gragas guide. with this guide you should have everything you need. much hp and mana and acceptable AD and AP.

Pros:
+survivability
+very long range
+pushes lanes easily
+good escapeabilities

Cons:
-not much AD/AP (~250-300 AD and AP) but still OK.
-fairly long cooldowns
-reather weak endgame

Happy Hour: On ability use, Gragas takes a drink restoring 2% of his max health over 4 seconds.
-great passiv. grants a long lane stayability.

Barrel Roll (Q): Gragas rolls his cask to a location, which can be activated again to explode or will explode on its own after 5 seconds, dealing 85 / 135 / 185 / 235 / 285 (+90% of ability power) magic damage in the area. Enemies struck by the blast have their attack speed lowered.
Cost 80 / 90 / 100 / 110 / 120 mana
Range 1100
-very long range. massive damage and extremly awkward for your enemy

Drunken Rage (W): Gragas guzzles down brew from his cask, channeling for 1 second. He gains 30 / 45 / 60 / 75 / 90 mana while channeling, and becomes empowered after finishing, increasing physical attack damage by 30 / 40 / 50 / 60 / 70, and reducing damage taken by 10 / 12 / 14 / 16 / 18% for 20 seconds.
Cooldown 30 seconds
Range 20
-very helpfull early game with the little mana boost it gives. very very good for endgame. grants +70ad and 22% damagereduction for 20sec.

Body Slam (E): Gragas charges forward, colliding with the first enemy unit he hits and dealing 80 / 120 / 160 / 200 / 240 (+50% of ability power) plus 66% of his physical damage to enemies in the area. Damage is split amongst targets hit. Units hit by Body Slam are slowed by 35% for 2.5 seconds.
Cost 50 / 55 / 60 / 65 / 70mana
Range 25000
-just like flash but it deals damage. great chase/escape skill

Explosive Cask (R): Gragas throws his cask to an area. Upon landing, it deals 200 / 325 / 450 (+100% of ability power) magic damage to all units struck, knocking them back and applying a 20 / 30 / 40% attack speed debuff.
Cooldown 90 / 75 / 60seconds
Cost 100 / 125 / 150mana
Range 1050
-deals tons of damage with 1.0 ap ratio. low cooldown and aoe effect

basic caster runes:

Greater Mark of Magic Penetration always pick as a caster
Greater Seal of Scaling Ability Power endgame boost
Greater Glyph of Scaling Ability Power endgame boost
Greater Quintessence of Ability Power early bonus

optional:
Greater Seal of Replenishment if you can't handle your mana
Greater Seal of Vitality if you want more hp endgame but i think you should have enough with banshee and RoA
Greater Seal of Armor good for earlygame
Greater Seal of Evasion even better endgamerunes than armor
Greater Glyph of Scaling Cooldown Reduction for more spamming action

9/0/21 ordinary caster masteries nothing special
but with 3 point in Expanded Mind for more mana for your Manamune and Archangel's Staff

• start with Doran's Ring or Ruby Crystal
  many people starts with Sapphire Crystal but i think its not necessary because you gonna spam your Barrel Roll which cost a lot of mana early game but with your Drunken Rage your will always have enough for another Barrel Roll. If you start with Ruby Crystal you gonna have more tankieness and get your RoA earlier. It also improve your passive.
• buy a Catalyst the Protector
• Boots
• Rod of Ages
  IMPORTANT: buy Archangel's Staff AND Manamune!!
  both gives you mana but the passiv dont stack with each other
• Banshee's Veil
  now you should have ~250ad ~250ap 2500hp 2500mana
• the 6th item is up to you. i prefer Hextech Gunblade but you can buy Rabadon's Deathcap as well or some tank items.

i use Ghost/ Exhaust
Ghost is a great chase/escape skill. in combine with Body Slam you can catch up most champs.
Exhaust gives you a better 1v1 situation and can safe your life or your teammate

optional:
many people use Flash but i think you dont need it because you already have Body Slam as a Flash replacement.
you can also use Ignite if you dont like Exhaust

stay in the brushes and harass your enemy with Barrel Roll
last hit with Barrel Roll
do everything with your barrel! he's your best friend!!

use Drunken Rage as often as you can. it gives you mana everytime you use it.

you may got some manaproblems early game. dont waste your Barrel Roll and everything will be OK. but if it bother you just max Drunken Rage before Barrel Roll. you will deal much less damage but your manaproblems should be solved.

Initiate with Explosive Cask and try to push some enemys toward your team. Spam your Barrel Roll. slow fleeing enemys with or protecting teammates with Body Slam. Your Drunken Rage gives you a lot more tankieness in teamfights and provides you more AD. Cast it before running into a teamfight.

farm with your Barrel Roll it should clear a wave with a single one. if not just Body Slam and wusch wave down.

hmm.. i never tested him in jungle but stonewall008 does so it seems to work xD
maybe i gonna play him as a jungler one day. just follow the route stonewall shows.

EDIT:
so finally play him as a jungler as well and i have to say it makes a lot of fun to play. kind of savely and fast. i followed stonewall008's route and TrevLinden16 item build.

he's a big fat mother***** damagedealer, tank, offtank and pusher.