Mega Inferno Bomb is excellent to ruin an enemy push: it can wipe out an army of minions and heavily damage several enemy champions, brutally ending any attempt to push and also giving you lots of gold. Wait for the enemy team to be as close as possible without risking to damage allied turret for maximum efficiency.
Bouncing Bomb has a fast travel time meaning it is a strong tool for harass especially when combined with Short Fuse to play the hit and run game.
Satchel Charge can be used offensively too. Placing it in the middle of your lane and walking around it will make your lane opponents scared of getting too close, as you can activate it for a huge leap. Satchel Charge combined with Hexplosive Minefield is a very powerful zoning tool, and can force your enemy to walk in the direction you choose, making it easy to land a Bouncing Bomb or a Mega Inferno Bomb.
Hexplosive Minefield can choke off large portions of jungle routes which effectively deters chasing enemy champions.
Bouncing Bomb's range is greater than the enemy's vision range when thrown at maximum range with three bounces. Enemies won't be able to see the bombs until the last second, so use this to effectively land Bouncing Bomb harass at a safe distance.
Later in the game, it can be upgraded into Boots of Swiftness giving you an easier time avoiding all of his spells.
With proper timing, Ziggs'Bouncing Bomb can be dodged by running underneath it in between bounces.
Try to avoid fighting Ziggs in the jungle, as Hexplosive Minefield can block off potential escape routes and the narrow pathways make it easier for him to land all his abilities, including Mega Inferno Bomb.
Ziggs deals mostly magic damage. Building magic resistance items will reduce your damage taken.
All of Ziggs' spells except Bouncing Bomb have a very long cooldown at early levels; engage him after he finishes casting his abilities.
Stay away from the center of his Mega Inferno Bomb, as the spell will deal less damage if you are outside the center. You can tell when where it will land by the circle it creates before it lands.
Keep in mind that spell shields will only allow you to avoid a single Minefield. All other will still detonate. Don't use spellshields to block that ability; instead save them for Satchel Charge or Mega Inferno Bomb
Ziggs main champion counterpicks tend to be assassins with strong gap closers. Ziggs is not very mobile, is squishy, and is reliant on abilities that are rather easy to dodge. For those reasons, champions like Zed, LeBlanc, and Katarina. They all have means of avoiding Hexplosive Minefield and killing Ziggs.
Apart from assassins, champions such as Vladimir and Nidalee have the sustain needed to shrug off Ziggs' poke. Nidalee also has the mobility needed to dodge Ziggs' abilities, while Vladimir scales extremely well into late game.
Other options to deal with Ziggs include: champions that can rival his range (Xerath, Syndra) or very mobile mages (Ahri, Kennen)
Ziggs excels at countering short ranged or melee champions that have weak sustain and no gap closers, including but not limited to Cho'Gath, Ryze, Swain, and Orianna. Avoid playing them against Ziggs.