Pros / Cons
Pro: Has an extremely strong team fight potential, arguably the best team fight champion in the game.

Con: However he's really weak in 1v1s.

Abilities:
Q:
If you Q is on a champion, it will bounce to ANYTHING you hit. Even plants, this way you can easily grab people that are trying to run away.

W: Your W is your main source of damage and also healing, make sure to use it if you want to survive.

E: Your E is your gank material, you jump on them, Q them, and they will not escape.
The area where you are jumping will be marked, so if the enemy is good, they will see it coming. That's why you should only use your E if they're distracted, or if you're next to them.

R: Your R is amazing, I often use R in combination with flash to make sure I get the most out of it. You can stun entire teams with it.

Combo's:
Zac has a LOT of combo's he can use, due to his kit, however if you're new to him, here are a few basic ones for ganking:

E > W > Q > Auto attack a different entity > W

Walk up to him > Q > Auto attack a different entity > W > E

Past 6= Add an R after the combos, during the R, spam your W.

Pathing
Zac is a horrible lvl 1 - 2 early gank cheeser, due his requirement of having both E and Q, however you'll need your W for clearing your camps.

If your laners are at least somwhat decent in the game, it should be a guaranteed kill when you gank past 3. Past 6 are free kills even if they're idiots.
Bottom left:
1. Red Buff
2. Raptors
3. Wolfs
4. Blue Buff
5. Gromp
6. You can choose between ganking bot, mid or scuttler.

Top right:
1. Blue Buff
2. Gromp
3. Wolfs
4. Raptors
5. Red Buff
6. You can choose between ganking bot, mid or scuttler.

Ganking
You are an incredibly weak character early game, however you're really good at locking down enemies from moving anywhere or using abilities, which means that your laner will just about always win the 2v1. However if you get counter ganked and the opposing laner is not at least below 30% hp, you might have lost the 2v2 already, as Zac isn't good at anything but tanking and locking down opponents. Try to always avoid being in a 1v1 situation with the enemy jungler.

Team fights
Your task in team fights is to lock down the opponents and not let any of them pass into the back line, you can easily do this because of your huge amount of CC, if any somehow do get past you, you can Q + Auto attack them away again.

Items
You should always try to build for Bami's Cinder, not only will this provide you more HP, it will also provide you more damage and clear speed.

Thornmail, you should always try to build this (unless they are Ability Power heavy), because it will greatly increase your damage and decrease their self healing.

Spirit Visage, you should always try to build this (unless they are VERY Attack Damage heavy), because it will greatly increase your self healing from your blobs.

My favorite legendary to build is Gargoyle Stoneplate, as it allows you to dive all in, without even shivering an inch.