Hello, and welcome. To my Gragas build. This build increases his tankyness and damage! That's right, both! So let's get started.
I get damage Marks specifically for Body slam, as it is your main damage output. I get health Seals and quintessences, with a 1.5% health quintessence. To increase my passive and "Atmas Impaler" 's effects. Finally, AP glyphs to give me extra damage on "Barrel Roll", "Body Slam" and "Explosive Cask".
9/21/0, is my Mastery build. This gives me addition Health for my Passive and "Atmas Impaler" 's effect. I also get 9 points in Offence to gain additional AP.
"Barrel roll" is a great poking ability early game, but if playing 3v3 (Or 5v5), and plan to get First Blood then learn "Body Slam" first, for a bit more damage and a slow. Get full "Barrel Roll" If you're planning to get "Rod of Ages" and "Rylai's Crystal Scepter". If you're looking for the more tanky way, go for full "Body Slam"s. Buying "Warmog's" and "Atmas Impaler" as your first 2 items. (Besides boots). Finally, obtain "Drunken rage" last.
"Doran's shield" is the best possible starting item for Gragas, if the enemy team is mostly AD. It helps his passive and gives him extra armor. "Ninja Tabi" or "Mercury treads", depending on which team has more (Aps' or ADs'). I suggest always getting "Spirit Visage" first, as it is cheap and helps your passive. Move on to Either "Rod of ages" and "Rylai's Scepter" or "Warmogs" and "Atmas Impaler". And as the final item, I suggest either a armor or magic resist item, or a "Rabadon's Deathcap" Or possibly another "Rylai's Scepter", to help passive and damage output.
Flash is always a good choice, ghost may be questionable. In 5v5, Teleport it also a great choice for Gragas. I get ghost to chase or run away, and hey. Who wouldn't like to see a fat man run?
Use "Drunken Rage" to kill creeps faster and to also grant you Hp from Gragas's passive. If Your Hp is low, and no one is coming out for you, either jungle to gain your Hp back (From passive) Or farm minions with abilities. Be sure to get some mana potions, Gragas has quite the mana issue if you are farming with abilities. Use Barrel roll to poke, but make sure that it lands in a way so that if the enemy get's away from it, it'll hit the minions.
So there you have it, that is my Gragas guide. I hope you enjoyed it!