Zac is very squishy and easy to kill off in the early game, but if you are willing to poke and bide your time, then messing up the enemy champ by slingshoting them and proceeding to rapid fire off his other abilities it can be very rewarding. However, keep in mind that while Assassin Zac has much bettter burst damage than Tanky Zac, he is much more susceptible to CC and damage, thus be ready to use Zhonya's when need be and try not to get caught un-awares by the enemy team. Although I would suggest against using Zhonya's while Ulting, as it negates his ult's effects, but it may be useful if they would have finished you off before finishing your Ult anyways.

Typically with Zac you want to jump in unawares to the enemy team, rifle off your q and w, then keep them crowd controlled with your Ult, while using his w to drain their Health, and then chasing after them, or slowing them using his Q, if you have the Health to do so.

Zac is extremely good in team fights and can typically control any situation as long as your team can come in for the fight. As a rule of thumb try to Elastic Slingshot from bushes or unseen areas as much as possible, but allow your team to know you are doing so, only use it in-lane or elsewhere if you need the knock-up, or if you know you can catch up to the enemy champion with it.

Typically you want to try to get as much farm as you can, at every calm time, or when you are not needed; however, I would advise going to anylane that you believe you could pick off a easy kill/assist in, as Zac is a fairly decent roaming champ.

All in all, Zac has a high damage out=put, is able to get past area other champs cannot, and has a slew of CC to back him up. However, Assassin Zac IS as squishy as he looks, so don't get caught off-guard, because stuns, snares, roots, and other forms of disruption are extra-hard on Assassin Zac. This can take a lot of getting used to in terms of timing, but can be incredibly worth when the opposing team starts to fear every bush and un-seen area.