Gragas has a surprisingly good amount of burst when you play him with Electrocute. You can very easily burst someone down if you all in at level 3, even level 2 if you can in some good damage with your Q. Your main clear with your Q is also your best poke. Once level 3 with you W you can hit all melee minions with both Q&W then move in on the mage minions and your lane opponent. Even without potions you can slowly regain a bit more health without leaving lane by just chucking your Q at the lane when your passive is up.

Your best burst comes from using Electrocute and Sudden Impact and all ining when you can. E->Q->basic or E->Q->W can very easily burst down your lane opponent when you're low level, making it easy for you to get early kills and snowball. Eyeball Collector grants a bit more power and Ravenous Hunter works well with you passive. Manaflow Band is essential due to your early mana issues, which is needed if you want to be able to all in after poking them out and clear wave. Scorch is more poke when you hit your Q and when you start to all in.

Rod of the Ages gives you all the things Gragas loves and needs; health, mana,and power. Finishing this time first will set you up for later in the game. Hextech Protobelt give more health and power, as well as more poke, and an additional dash to either engage or run when your E is down. Ionian Boots of Lucidity give cooldowns which are important for your overall combat ability. Without abilities up, you can't really hit your opponent when they are behind their lane, and if you start to get ganked, having your E & R up helps you get out.

Maxing your Q first helps with you overall poke and lane clear. Mostly the clear, with your W you can hit all melee minions if they are positioned right, but you don't wanna get caught out if you try to basic or W the mage minions. Maxing your E next is good because it helps with your burst when engaging and lowers the cooldown, allowing you to engage more and get out quicker if you start to get closed in on.

Flash is, Flash. You have it on pretty much everyone. Ignite is good for a little bit of tick once you start to fight or if they are about to get away with just a little bit of health but you already used all your abilities, burn them.