Zagara is, relative to her power, pretty inarguably the most underplayed character on the Alpha servers. I'd at some level say that this is because she doesn't really work the way you'd expect. You see that 'Specialist' type and assume she's just about pushing lanes and doing her own thing, but she's actually able to put out impressive hero damage when it comes to both big fights and more limited encounters. Her main flaw is actually one of her advantages, her abilities have a low enough cooldown that she can kind of just exchange her whole mana bar for doing things incredibly fast then be forced to retreat and regen.

I'll start with a general discussion of her abilities, then go over her talents in detail, then discuss a few reasonable builds.

Zagara is rather unique, in that every single one of her abilities generates a Zerg creature with physical presence on the battlefield. This has interesting implications for some of them that we'll discuss as we get there.

Creep Tumor - (Combat Trait) Creates a Creep Tumor that burrows underground and generates Creep for 240 seconds. You and your minions move faster on Creep, and regenerate health. They also have sight, which is their main use. Drop them in sight blockers to cover your flanks and around anything you might want to know if the enemy approaches.

Baneling Barrage - Zagara's equivalent of a Skillshot. She releases four Banelings in the direction indicated that will explode on death, contact with an enemy, or at the approximate end of the skillshot indicator. Their explosion has a pretty decent radius, and since they are actual minions and not a visual they'll also eat up tower shots which can be nice.

Hunter Killer - Summons a Hydralisk to pursue and attack an enemy target. This can do surprisingly large amounts of damage and has a reasonable range. It's a great tool for putting pressure on an enemy hero, especially if improved with talents.

Infested Drop - A Zerg drop pod falls onto a target area after a brief delay, damaging targets and creating a pair of Roachlings. They're relatively weak, but every bit of damage counts and two extra bodies is never a bad thing.

Devouring Maw - Zagara's first ultimate. Targets an area, and after a short delay a huge thing rises from the ground and eats everything in that area. Does moderate damage, and leaves the targets incapacitated but invulnerable. While the Maw is invulnerable, it does have a physical presence and will block movement. Be careful not to body block your team with it, that's always very embarrassing.

Nydus Network - Zagara's second ultimate. I really want to love the Nydus Network, because it's so close to maybe being great. You create Nydus Worms that allow you to travel between them. Entering a worm is significantly faster than a hearthstone, so this can be a good way to escape. Always have one at the Core, because that will allow you to keep your mana high and your escape options strong. They can also facilitate quickly moving between lanes. The downside is that you have to physically go where you want to place them, and they are killable (indeed things like Grave Golems consider them buildings and will stop to attack them).

Obviously we'll look at talents by tier.

Tier 1:

Centrifugal Hooks - Banelings travel twice as far before exploding. This is actually a pretty okay talent, and is a pretty reasonable choice if you're taking Nydus Network and can take the other Baneling talents.

Corpse Feeders - Roachlings get extra duration when they kill things. This won't happen very often, so I really wouldn't suggest taking this.

Reconstruction - Increases regeneration on Creep from 200% to 300%. It's okay but not great, you've got much better regeneration tools than Creep.

Demolitionist - Basic attacks do more damage to structures and destroy ammunition. Increases your ability to deplete structures of ammunition, and is just in general pretty useful. This and Centrifugal Hooks are the only real options.

Tier 2:

Envenomed Spines - Increases basic attack range and adds a damage over time component as well. This significantly increases the damage you do with basic attacks, and the extra range never goes amiss. A pretty solid choice for sustained damage.

Medusa Blades - Causes your basic attacks to rebound to up to 3 nearby targets for reduced damage. In theory it's more damage than Envenomed Spines, but spread out over multiple targets. The lack of increased range really hurts it, though.

Tumor Clutch - Eliminates the mana cost of Creep Tumors and reduces the charge cooldown on them. The mana cost is generally not an issue and you have plenty of charges as is, so this isn't really worth giving up the extra damage of the other talents in the tier.

Envenom - Puts a large damage over time effect on an enemy. A solid choice to improve your burst damage, if that's how you want to build. It'll amount to less actual damage done at the end of the game than Envenomed Spines, but sometimes you need to pop a big DoT on someone as they try to run and this is that.

Infest - Increases a lane minion's damage by 400%, has two charges. If this worked on mercenaries and summons and such this would be interesting, but as is you're giving up some really good choices for something kind of weak.

Tier 3:

Battle Momentum - Basic attacks reduce the remaining cooldown of your abilities by .5 seconds. If you hate your mana bar even more than usual, this is a good way to deplete it even faster. It's probably not a great idea, though it could work with Nydus Network.

Volatile Acid - Increases the damage Banelings do to non-heroic targets by 50%. With this Banelings will really brutalize enemy minions, mercenaries, and structures. It's hard to take without taking Nydus Network, though, because it competes with Zagara's best talent.

Ventral Sacs - An extra Roachling spawns from the Infested Drop. If you really love Roachlings and again took Nydus Network I guess this isn't 100% terrible but it's kind of blah really.

Endless Creep - Creep Tumors spread Creep faster and farther. Just don't, friends don't let friends take talents like this.

Rapid Incubation - Zagara channels for several seconds, regenerating health and mana. Has a moderate cooldown. Helps alleviate Zagara's mana issues, and therefore is largely mandatory unless you take Nydus Network.

Tier 4:

Ultimates - I discuss what they do above. Both are reasonable choices, but Devouring Maw is definitely better at the moment. I suspect they'll buff the Network in some way, because it's just a bit unwieldy to actually get going.

Tier 5:

Mutalisk - Hunter Killer now spawns a Mutalisk instead of a Hydralisk. Mutalisks fly, last 50% longer, and have a bounce attack. A reasonable choice, it's less bursty than the other Hunter Killer talent in this tier but is a bit better at pursuing since it flies and lasts longer.

Grooved Spines - Increases the range and damage of Hunter Killers. Makes an already pretty powerful skill even nastier.

Bile Drop - Effectively doubles the damage of Infested Drop in the form of a DoT for its initial damage on any target hit. It's a kind of blah choice, it can be a real pain to actually hit anything but NPCs with Drop given its delay.

Giant Killer - Adds 1.5% enemy max health to your basic attack damage when attacking enemy heroes. It's the sort of thing that's always an option, though it's not how I prefer to build.

Spell Shield - After taking ability damage, reduce the ability damage you take by 50% for the next two seconds every 30 seconds. A solid survivability upgrade, and therefore always an option given how squishy Zagara is. If you're having trouble surviving an enemy comp, consider it.

Tier 6:

Baneling Massacre - You now summon eight Banelings with Baneling Barrage. If you've got Centrifugal Hooks and Volatile Acid this can cause some crazy damage to things that aren't heroes, but it does root you in place for a bit to channel it.

Brood Expansion - You now have two charges of Hunter Killer. There's no cooldown triggered by using the first charge, so you can spit out two of them on someone almost at the same time. Combined with one of the previous tier's upgrades to the ability can allow you to really ruin someone's day, and sometimes get you hilarious revenge from beyond the grave on someone who killed you but was at low health.

Metabolic Boost - Increases the move speed bonus of Creep to 40%. Makes escape easier if you've already got Creep set up but you're giving up some really good talents to take this.

Stoneskin - Shields you for 30% of your max health for 5 seconds, on a minute cooldown. Again, if you're feeling like you want more survivability this will certainly give it to you, at the cost of some damage.

Tier 7:

Fury of the Storm - Your attacks bounce to nearby enemies for half damage. You've already got a talent like this earlier and you shouldn't have taken that, and you also shouldn't take this.

Bolt of the Storm - This lets you teleport a moderate distance on a moderate cooldown. This gives you some escape capability you are sorely lacking, and is what you should take full stop no questions.

Tyrant Maw - Increases the damage of Devouring Maw and causes the cooldown to be reduced if an enemy dies within it. The problem is that it's just really hard to make that happen even with the increased damage, so you really shouldn't go for this.

Broodling Nest - This talent is really, really hard to get any use out of. When you leave a Nydus Worm, six broodlings pop out. This has a 20 second cooldown. The big problem is that you'll often be fleeing to the Core with your worms, which will waste the broodlings. You could enter and exit a single Worm to game this, I suppose?

I provide several builds above, but there's really quite a lot of variation possible. The General Use build I provide is what I mostly use, it focuses heavily on damage (though I take Envenomed Spines for sustain and range instead of Envenom, which I'm not the biggest fan of despite acknowledging it's strength). The main thing is that you really should take one of Rapid Incubation or Nydus Network, otherwise your downtime to recover mana after fighting will really be killer. The demolitionist build there is an example of a build that relies on Nydus to recover mana, just remember that you're giving up one of your team fighting tools if you don't take the Maw. The third build is a more defensive option, again you can swap Spines for Envenom if it's more to your taste.

Just remember as you play, you're quite fragile and not terribly fast, so don't get reckless. Keep an eye on your mana and your escape options clear and the Swarm will conquer all your enemies.