This guide is for tank Gragas, I find building him as a tank to be a lot more viable than AP (I have yet to test out a DPS Gragas, but I dont think it will be as good as tank)
Gragas can be one of the most durable tanks in the game due to his Drunken Rage reducing damage by 26% at Rank 5.
Runes: Health/perLVL= Red Runes - Dodge= Yellow Runes - Blue= Health/perLVL
(I personally do not know if this is the best bet for runes because I dont have a very good tank page, but this is what I would probably go)
Masteries: 1/21/8 (May change slightly based on what summoner spells you take)
Summoner Spells: I personally use Exhaust/Fort to be a little more useful for your team, exhaust is great for early kills or shutting someone down in a team fight and Fort because you are so far into the Defense tree you might as well.
Clair, Flash, Teleport, Ignite are decent secondary choices as well.
1. Body Slam
2. Drunken Rage
3. Drunken Rage
4. Body Slam
5. Body Slam
7. Drunken Rage
8-18 Priority Ult > Drunken Rage > Body Slam
I find if you do not get atleast 3 points in Body Slam you move too slow and it deals too little damage.
Item Build: (Feel free to sell Doran's Shield/Heart of Gold when you need to)
1. Doran's Shield(Safest Route), Ruby Crystal, Mana Manipulator (Lane partner is mana dependant)
2. Boots -> Ninja Tabie or Mercury Treads (You decide based on the other team)
3. Heart of Gold
4. Giant's Belt + Mana Manipulator > Soul Shroud
5. Aegis of the Legion
6. Glacial Shroud >Frozen Heart
7. If game is still going on Sunfire Capes or Guardians to finish the last spots
Mostly you are just stacking Auras to support your team ,but when you reach 40% cooldown reduction your drunken rage has a 27sec CD and lasts for 25 sec so it's almost always active and you will be surprised how well you can take hits
Laning: Spam Spam Spam. Use Drunken Rage whenever it is off cooldown and use Body Slam as much as possible to last hit or harrass melee champions. More spam means more HP regen from your passive and Drunken Rage's mana will keep you laning for a
Using Gragas' Ult: 1. Push people into your tower than body slam the weaken creeps so the tower switches to your target 2. Interrupt Katarina, Nunu, Fiddle, or toss at a twitch to knock him further away or closer to your team 3. Split up the enemies giving your team brief moments to kill the closest/weakest 4. Take down runners 5. Etc many more uses just a few useful ones
Mid: A few teamfights and pushes are just starting. Activate Drunken Rage prior to your team engaging (it lasts 25 sec) with drunken rage active your body slams will do a decent amount of damage. So rush into the enemy team (making sure your team follows) and body slam away, toss your ult in the most effective away if you can.
Late: Drunken Rage is almost always active and you should be able to take a lot of damage! When pushing or defending make sure to go in first spam slam as much as possible and ult efficiently ,but dont be conservative your ult is only a ~35sec cooldown at this point.
Dont be afraid to die! Sometimes being suicidal is the only way to get the enemy to focus Gragas if your life ends up getting 2+ of the enemies killed than it was worth it.
I don't think Gragas is on the same level as some of the other more useful tanks ,but he can be a refreshing change of pace and a b*tch to kill.
I hope this was somewhat helpful and any comments/feedback is appreciated