Hello there! Let me start of by saying that Gragas is really, really good! He is not overpowered, nor underpowered. He's a fun, balanced champion! But he needs alot of farm as an AP carry.
You should ALWAYS try to go solo, either top lane or mid!

I take these runes because they give you alot of lain-sustain in the early game! The magic pen will help you farm and harass in the beginning, the mr seals combines well with his W and the glyphs and quints are good for his overall AP!

As Gragas, you always want to go SOLO top or mid! This is very important for your farm and early game! In a solo-lane you can set up ganks with your jungler that you can initiate with your ultimate, and after that his passive regens his health, he's good against two champions. You will be able to poke your enemies all the time while farming, which leads to a won lane!
Teleport will help you get there in case of that you die or just went B! You can also tp to bot lane for a kill!
Flash is just OP.

Pros!

High lane-sustain
high damage
Really good in teamfights!
Good ultimate
FUN

Cons!
Needs farm
takes a while to learn his ultimate
meele

You need to get the blue buff as often as you can, this is the best way to get high mana reg and some more cdr!
In team fights you can wait a little bit on the outside and throw in your barrels! After 1/2 barrels you can go in and start attacking! You may not be an AD character but thanks to your W you will get that +70 AD! That's really, really good! So you can go in and use your Body slam and barrel to do huge damage!
If you see some1 running of you can either throw them back in your team or execute them with ultimate + barrel!

When ganked you can use your slam to get out, and if you have to, flash and ultimate!