I start dorans. if this doesn't work for you it can be changed with boots pots or bottle pots, but i think it works very well.

Gragas pretty much has to wait until lvl 3. once 3 you can do your combo:
body slam and throw barrel, attack and pop barrel, attack again, and retreat

*body slam does reduced damage if it hits multiple units so make sure to do this when they are away from creeps.

use w every cool down!!!! unless if unsafe to do so

Max "w" second. this is more important than you might think. Gragas is pretty naturally tanky because of this. it gives more mana per use. And it gives ALOT of ad. your "e" has an ad ratio. so by scaling "w" you also help your "e" as well. Your attack will be strong to make csing very easy. and dont underestimate its damage on champs. with the combo 2 attacks of +60 ad hurts alot.

This is where gragas excels. once you hit 6 you can pretty much kill any mid from 3/4 or lower. some even full depending on their hp and resistances.

At this point you do your previous combo shown in early game. follow up with a ult knocking them directly behind you. if they haven't flashed be careful to time it right. once they are behind you they will most definitely flash or run because they are ~1/4 hp if not fed. proceed to auto attack them while waiting on skills. if they can get away by using their flash, let them. don't waste yours farm some creeps and let them back, your ult will be back up before their flash.

at lvl 9 gragas can 1 hit mage creeps with "q" this is how i farm most of my cs safely.
i make it really difficult to gank me. stay far unless your going to try to trade or poke. also can do about half of meele minions hp, making it easy to kill two of the three from max range if need be.

wait to kill mage minions until the enemy champ is next to them. sometimes you can get lucky and get some free poke. but don't waste your time trying to land a long range barrel.

Gragas can gank bot exceptionally well. leap over walls to save time. and land an ult over wall to thrust enemys out of tower, or toward you allies.

gragas damage is great, however it does fall off a bit in late game. you will need to focus more of your spells onto the adc and apc to be more usefull in a team fight.

ap gragas has poke, but is NOT a poke champ. is q is pretty easy to dodge when facing him in lane. sometimes you can hit a few so its worth to throw it out there, but dont rely on it. worry about body slam -> barren -> well positioned ult

Why do i say well positioned. Some people hate gragas with aoe comp. i love him. but one mistake can mess up an entire team fight.
If they initate the team fight and you team is not set up for one. then use it to disengage and damage.
if your aoe comp starts their spells, save you ult for a second then use it to try to keep them from escaping. obviously throwing you q to assist the fight. if your aoe team used their skills already, feel free to hit as many as you can with your ult. just don't save them by pushing the survivors away from your team.

Their are some situations where you ult can hit a stragglers to get them more grouped. Gragas's ult is on a fairly short cd, especially with unholy grail and blue buff, so dont be afraid to use it.

why be tanky when you can be invulnerable- (hourglass) dont build tanky, build apc, outplay them with hourglass.

barrels slow attack speed. don't be afraid to 1 on 1 a bruiser or adc mid game.

you can pop barrel when ult hits and have the dmg at the same time. can anyone say 1400 magic dmg dragon/baron steal?

people underestimate gragas's damage. bait moar.

ult enemy into tower followed by body slam. they die faster.

you can hourglass mid body slam and still finish it. charging fat golden statue = gg.

solo blue lvl 5 not much hp loss.

if your half hp no pots. stay under tower and throw barrels for creeps, body slam no where, w every cd, keep casting spells to keep you passive going.

Even fat men can be teemos. put a barrel down a few seconds early before they walk into bush, pop it with body slame, and your barrel will be up again!

attack speed reduction on dragon makes it much easier on jungler. help a boy out.