A key piece of advice I want to put in your mind as you play Zac: Imagine yourself as your team's big brother. Take the mind set you're already a big bad fed guy, and you just wanna help out your lil bros bulk up and get swol like you are. Everytime you engage it should be with the mentality of lowering the draw bridge for your allies to follow. During the middle of everyteam fight, you should be waiting for an opportunity for your ally to go in for a kill, and for you to retreat (with enemy aggro) or unstick yourself from the soon to be dead enemy and reattach yourself to the nearest threat.
This mentality will keep you alive far more often, and give your team the synergy it needs to over take objectives. Zac deals his dmg sustained throughout periods of time , the longer he survives, the more dmg and disruption he brings. A fed Zac is a liability to his team. This simple "frame of mind" advice should do more for you playing Zac than any guide. You should absolutely learn how to play Zac mechanically, you need to really, but after you accomplish that comes the next deeper level of understanding Zac. Why are you playing Zac, as opposed to jungler B, or C? Because of his unique role, niche, and dat body. Wiggle wiggle wiggle.