Zac is a high sustain, beefy, tank who excels in dealing great AOE damage, awesome cc, one of the best initiators in the game, and practically unkillable late game.

Magic Pen Marks
Armor Seals
Magic resist Glyphs
Magic Pen Quints

0/24/6
taking all health and health regen masteries, armor and magic resist, tenacity, and minions and monster reduced damage in the defensive category
take movement speed increased ward view, and increased health pot durations

pros:
extremely beefy
one of the best initiators
awesome sustain
mobile for a tank
low cooldowns
cons:
slow early game
weak early game
blob-lets become harder to save late game
no damage late game

as Zac, use your AOE and your low cooldowns to clear jungle camps and minion waves faster. Once you get your Spirit Visage and you Spirit of the Ancient Golem, your skills will be up at least every few seconds, so you can spam the hell out of them. In the jungle, you can either start red or blue, it doesn't really matter. I start blue for the low cooldowns so I can break my W key by spamming Unstable Matter.

the purpose of Zac in any game is to soak up as much damage, ultimates, summoner spells, etc so your team can deal damage to the targets. If you die after an initiation, that means you have successfully done your job, and its the matter of your team following up

People build the weirdest things on Zac, hoping that they would work, when they never do. Don't listen to the people who say build Spirit of the Spectral wraith because you get ap and cooldowns, you won't be tanky. Same goes for Amumu. I see the most ridiculous things on Amumu, and then they complain saying Amumu is too squishy. Well yea he'll going to be squishy if you build Boots of Swiftness and a Spectral Wraith! But I digress. Dont build damage, thats not your role of the team.

when Jungling, max your W (Unstable Matter) because it does more damage to monsters and minions. Then Max your Q (Stretching Strike) for more AOE and a bigger slow. Finally Max your E (Elastic Slingshot) because you will only need for initiation, since it went through many nerfs, reducing its damage. However people can still be knocked away from it, but it doesn't scale with level

I take Flash and Smite, because you are already pretty mobile with your E and your Boots of Mobility, but your E isn't always gonna be their for you, so I take Flash if im in a dire situation and my E is on cooldown

Zac is one of the best initiating tanks in the game, if not the best. Early game he may be kinda squishy, with moderate damage, but once you get your items, you will be practically unkillable