Zag is now a really strong teamfighter and global presence, I would argue that she is now a stronger teamfighter than before becuase of her new slow.

Zagara has very few bad talent choices, so the challenge lies mostly in getting used to the synergies and picking the right build based on your opponents.

Level 1
Volatile Acid: Your banelings are there for clearing waves and slowing enemies. The extra damage is not neccessary as you can comfortably clear lanes without it. Steer clear of this talent.
Corpse Feeders: This talent makes it so that you always have roaches while clearing camps, and for draining ammo (Only 3 roach drops with this talent will drain all ammo from an entire gate). Apply roaches liberally!
Infest: Great for split pushing, and will help you clear lanes a little bit faster, but in my opinion an inferior talent to Corpse Feeders.

Level 4
Envenomed Spines: Avoid this talent. Lower potential than the other talents, both as a split pusher and teamfighter.
Medusa Blades: Viable if you plan on split pushing most of the game. Although a case could be made for the Serrated Spines talent even so. You waveclear are amazing even without this talent by just using your untalented banelings.
Serrated Spines: There will almost always be heroes around for you to stack this up pretty fast, making this the goto pick for this talent tier.


Level 7
Baneling Massacre: Since you now have charges of banelings this talent is probably only viable should you pick up Devouring Maw at lvl 10. The damage potential is not that great and you would probably benefit more from either of the other two talents.
Viscous Acid: Spread your slow and watch your enemies struggle to reposition. This talent is my favorite as it just makes your and your team's job a whole lot easier. You can also use this talent to make for an easier getaway when enemies are chasing you.
Bile Drop: If you're facing a double warrior comp, then this talent might be good for you as you would have plenty of good targets for this to stack up. It also synergizes well with Devouring Maw. Basically pick this up if your team is low on damage, although keep in mind that you will sacrifice the utility that you would've gained from Viscous Acid.

Level 10
Picking your ultimate as Zagara is something that you should probably have decided before level 4. Devouring Maw is an amazing CC that even reduces the duration of abilities such as Metamorphosis. Nydus Network on the other hand will give you global presence, but also battle momentum, which for Zagara means more hydras and more roaches everywhere!
Devouring Maw: Pick this up if you are afraid of their dive potential, or if the enemies have a tendency to clump up like with double tank (allowing your team to move in on their backline).
Nydus Network: Pick this up if you like damage and winning. #winning #JustDOIT
Placing your nyduses are no longer as critical, but try learn where to place them on each map in order to maximize on your potential

Level 13
Hydralisk Transfusion: Only ever pick this talent if you're not worried about getting nuked, the enemy does not have mages, and you have a hard time keeping creep spread. This makes it so situational that you can basically ignore this talent most of the time.
Protective Coating: If you're playing Zagara you should have creep underfoot (under-claw?) always. This talent is basically 20% reduction in incoming damage.
Spell Shield: Pick this up if you're having issues with burst damage from mages like Jaina AND you are having issues spreading creep. (Although you should be able to spread creep even while in a TF)

Level 16
Brood Expansion: Go to talent. With Nydus Network you suddenly have endless hydras.
Corrosive Saliva: Up against double tank? Pick this up. See Diablo on the enemy team? pick this up. Otherwise steer clear.
Mutalisk: Pick this up if you have a lot of obstacles keeping your hydras from getting their damage in. For example while playing on a map like Dragon Shire where there is a lot of terrain and structures.

Level 20
Tyrant Maw: Meh. You dont pick up Devouring Maw for its damage anyways.
Endless Creep: More movespeed making ganks impossible, and now your Creep Tumor range equals that of Azmodan's Globe of Annihilation. Use this range to scout out enemies before entering a location.
Fury of the Storm: Simply a decent damage buff, no utility. Pick it up if you're winning or if you picked Devouring Maw.

The basics to playing Zagara is simply to be prepared.
Spreading creep is the core of her kit as it boosts your defense by granting you vision of the enemy team, making ganks a lot harder, while also boosting your movement speed which allows you to run away from any gank. Or if you're winning the teamfight you can catch up to the enemies running away.


Lets go over some situations to see what you should be doing:

Laning Phase:
Spread creep and push lane.
You can easily clear waves by standing in the wave and using banelings on top of the caster minion.

Roaming:
Spread creep.
Roaming with Zagara is not very useful until lvl 10 when she gets her ulti, even then it would probably be better to split push.

Late game:
Spread creep and split push when it is safe.

Teamfights:

1. Spread creep
2. Spread slow among the enemy team with your banelings
3. Use Hunter Killer on enemy heroes (preferably squishies to zone them out)
4. Try to get as many basic attacks in as possible to get your stacks up.