Always play aggresively. Get your teammate to help you get blue. Take advantage of being a burst mage. Spam Bouncing bomb, and try to go for good combos. When playing against somebody like Karthus in mid lane, your biggest advantage is constantly wearing them down with your q. when they get low, go in for the kill; using all of your abilities. if they get away, no problem for ziggs, use your ultimate then return to base to shop.

The only thing i can say is SAGELY SPORES. (elixer of brilliance). So many ap characters out there don't use them, which is plain stupid. The early AP is insane, plus it leaevs you enough gold for quite a few health/ mana pots.

Once you have slaughtered mid lane, immediately check top and bot lanes for a gank. If mid feeds you, you are an exceptional ganker. lead with minefielf then spam your Q. Use satchel charge to knock them back to you if they get to far away. Finish off with Ulti if necessary.

Ziggs is a great burst mage farmer. Throw your mines in a group of minions, then throw a bomb. get your gold and get fed.

Ziggs has awesome combos... Ill give you a few.

Throw minfeild behind them then spam Q to force them into it. (basic)
Throw minefield in front of them then use satchel charge to blast them into it. Start spamming Q. (intermediate.)
Satchel charge yourself out of the brush (for surprise) thro minefield behind them, and spam q. use passive to your advantage. throw your ulti FTW. (awesome)