Passive: Cell Division
This passive is what makes Zac such a monster in lane. The Health gain basically makes his spells free if you can pick up the cells as they drop. Be careful though, the enemy can destroy the cells by stepping on them. The enemy can attack you when you go for them if you make it obvious where you're going as well. The Revive part of this is great for early game, but it kinda falls off in teamfights as its really easy for your blobs to die to stray aoe spells.
Q: Stretching Strike
This is Zac's bread and butter ability in lane. You use it to farm and harass. It's on a short cooldown so as long as you grab the cells as they drop you should have no problem harassing with this every time it's up. Keep in mind it also slows. The attack is a little slow to come out though, so make sure you lead it just a bit. I max this skill first.
W: Unstable Matter
This ability is Zac's health shred. It's an Area of Effect Ability and it's on a short cooldown. So, why don't I max this first? The range on it is very short. It's just slightly larger than auto attack range, while your Q has a much larger range. Also, your Q usually out Damages your W in lane. However, if you enemy is obviously going to stack health, then max this first. Otherwise, max it last. Keep in mind you can use this ability while ulting.
E: Elastic Slingshot
This is Zac's initiate and it's one heck of an initiate at that. This ability has a small charge up time for it to reach full range and if you move it cancels the channel. If you let the ability cancel out, you get part of the cost refunded. Also, you can't launch behind you so make sure you're facing the way you want to jump. When you land you deal damage in an aoe and you knock up the enemy for a short time. The range on this ability increases as you level up. If you see a gank comming, just charge up this up and launch over the ganker's head, just keep in mind you can be cc'd out of this, so be careful. I max this second.
R: Let's Bounce!
Zac's ult Does AOE Damage, knocks the enemy up, and slows them for one second on the first bounce they are hit by. Any subsequent bounces just deal damage. Your ult is good for chasing or escaping, as your ult gives you Movespeed and Tenacity. It's only downside is the Cooldown is kinda large, though it isn't too bad.