As ziggs, Look for extended trades and keep auto-attacking him as much as possible.

Go for an aggressive play at level 2 with your W.

Stand outside of the minion wave at all times so zigg cant q you and push at the same time.

Your level 6 is stronger than his. Force him to over extend and then all-in him with your W, E and Ultimate.
 As ziggs, Look for extended trades and continue attacking it automatically as much as possible. Go for an aggressive level 2 game with your W. Stand outside the minion wave at all times so zigg cant q you and push at the same time. Your level 6 is stronger than his.