Playing Zac Sup is all about engaging at the correct time, & of course landing those engages. Common sense engage tactics are still relevant here: make sure your ADC/team is able to be in position to follow up, punish the enenmy laners if they stray too far from one another, try to jump/engage from out of vision(out from a bush or behind a wall).

Getting lvl 2 before the opposing bot lane is a massive advantage in general, Zac capitalizes on this better than any champ in the game. You get level 2 first by autoing the 2nd wave as much as possible when it comes in(use your shares on the melee minions closest to 1/2 health for maximum value). If you aren't duoed, try to communicate that you want to push for 2 first & let them know you will be all-inning the immediately. Once you have 2 go for a E/jump on the ADC(Sup is ok too if it's much more guaranteed). Once you land, Q/sticky arm both the ADC & sup together(it's okay to Q/sticky a minion if the other laner isn't in range. Ignite once landing your combo to the cut the likely enemy heal. Don't forget to auto + pickup blobs after landing CC.

Vision control + matchups will dictate how aggro you should be playing. You need to control vision in bushes, both so you can jump somewhat undetected & to invite ganks from your Jungler/Mid. Try to gank for your Mid & secure things like scuttle & dragons with your Jungler.