Woody Fruity Combo:
Basically you throw you Q out in any direction you want and engage to enemy with you W + E combo. then right when your target is out of the knock up throw your ult/R so it will knock you target into your Q you threw at the start, and pop the Q once your enemy is over it.

This is a very hard combo to mastery, but once you can do it with ease it is a great combo to kill any enemy.

the only down side to this combo id that your Q only lasts 4 seconds so you have to act fast if you want this combo to work, also you have to be ready to pop your Q or you might not kill the target and you will be left with no escape because you just used all your abilities.

Example: https://www.youtube.com/watch?v=wGNna1x_LjU

Combo with out your ult:
This a simple combo that is less complicated than the Woody Fruity combo, all this combo does is us your maximun bust damage with no ult.

All you have to do is use your W then engage with your E. While you are in the animation of your E, you can still use Q , so while your in the E animation your roll you Q to your target and once you hit the enemy with your E and W you pop you Q. If you have thundlords it will proc all you target will be slowed at the end because of your Q.

Flash E:
This ins't a combo, but this took me a awhile to figure out. While you are in your E animation you can flash. If you are close enough to a enemy and you can flash on top of him/her, him/her will be knocked up from your E. From there you can do any combo you wish. This took me awhile to figure out because once you flash you stop your E so you cant go any farther than your flash. You can uses your E and travel pretty far before flashing so it is a very big gap closer for ganks and combos. Using this mechanic in the Woody Fruity combo and be very useful since you can't go through minions to E a enemy (Also this looks very cool and makes you look like a pro Gragas).

Usually on the first clear ill take the first camp and the closes buff and improvise from there. If I got a great leash the then enemy jungler doesn't usually invade early, ill go ahead and take wraiths/wolves. If I got a fine leash and after the closer buff im at about half health, ill skip wraiths/wolves and go straight to my other buff. Form their i want to gank so i usually take the closes skutle crab and gank a lane i want to snowball or punish for pushing.

vs. Lee Sin, Shaco, or another early game jungler, I play it very safe and skip my first buff and go straight to wrathis/wolves then my other buff so they cant counter jungle me.

Gragas isn't a great early game counter jungler, but once you get going, counter jungling is very useful.