Well, for starters, avoid your minions. Zigg's Q can bounce over targets, including champions that position themselves correctly, and is relatively easy to dodge, but Minions don't dodge. So minions explode the Q and you take damage from it.
As a Jungler, I assume you'll be looking to Gank him. Watch for him to use his minefield, then you can go in on him. He'll try to satchel charge away from you, usually by placing the Satchel Charge in front of his escape path, walking over it, then detonating it. If you can stun him on the wrong side of the Satchel Charge, it can actually hinder his escape.
Another thing you can do to make Ziggs's life miserable is get that Air Drake. Poke mages hate trying to hit a target that's zooming around at Mach 3, because it's often a lot of wasted mana. Any Air Drake you can get will make it easier to avoid his poke and collapse on him.
One thing to keep in mind is that Ziggs is generally strongest early game, when you've got to stick around for long periods of time and can't really burst him down. As the game goes later, he loses a lot of power, since he doesn't really have a burst, his dash is slow, and all of his abilities are super telegraphed.
I main
, and when I face up against a Ziggs I know that I'm going to lose the early game. He'll poke me down, he'll blow up my tower first, he'll try to cut off my jungler's ganks, he'll land Q's on me while I'm charging my Q's, etc. But Mid to Late game the tides turn, and he's less happy with the situation as my Q's travel faster than his and can chunk him for half his health.