Ziggs
(Early Game)
In early game I usually buy Doran's Ring, sometimes I buy mana potions depending on who I am laning against. Ziggs AD is a little better than Fiddlestick's. (Fiddlesticks early game AD is AWFUL.) So you want to make sure you last hit all of your minions. And you can occasionally use your Q on the minons but know that your mana isn't the best early game. Make sure you save up to buy Arch Staff first. Then depending on who you are laningyou could buy Raylais. Just try not to feed the other team or get ganked.
(Late game) Ziggs can't do anything up close. The combo I use if I get ganked is , W, E, R. I use W to bomb myself as far away from them. Then, I throw down my E to slow them, and my R to get massive amount of damage on them. (Ziggs Ult can be very effective in team fights.) And if they have very little health I use my Q and that usually finishes them off.)
(Team Fights) Usually in team fights champions are all right next to each other. Either all killing 1 or 2 champions or just waiting for a fight. This is where Ziggs can show his true abilitys. I usually Q there whole team, then I use my W, and then E. I try to aim it towards their ADC or AP champions. Never use all your spells on their tank. And let your team help you and once they are all weak or close to weak use your R. Keep scaring the off with your Q because the cool down reduction is 5 seconds. And it does a massive amount of damage.
Ziggs champions that he can bully.
Ahri: Ziggs Q and W bully her down the lane from my experience.
Teemo: Teemo cant handle Ziggs late game. His Q does MASSIVE amount of damage and he's super easy to kill.
Thresh: As long as you dont get pulled you do a lot of damage to him causing their support to fall apart. Try to stay away from Thresh and get behind minons.
There is alot of more champions that Ziggs can counter easily but those are the most vulnerable.
Champions Ziggs cant handle Early game or late game.
Fizz
Blitzcrank
Udyr/WW
Mater Yi