EPT
Basically before I begin writing the guide, I want to let everyone know something about this match-up. This is IMO the most micro/macro intensive match-up there is in SC if both are decent players. Macro and Micro should be up to par unless it gets to a point where zerg has ultras, and even then you still have to take good care of your units, especially if you are out upgraded. Which leads me to another point. Upgrades are VERY important. Being down in upgrades, especially late game can cost you everything you've worked so hard for [the game]. Also, this is only a broad guide. I cannot be specific on when they will drop, expand, attack, etc... so you must be able to adapt as needed.
The Start
Every game begins with the creation of another worker and the split. ZvT is no different [don't forget to scout with your overlord; where you send it depends on your preference and map positionings on the map]. Continue to make drones until 9/9, and this is where the builds will differentiate.
Normal 9 Pool
This is a good variation build for those who want to mix a little something in their game. This build allows you to put pressure on your opponent at the very start and for those terrans who like to scout you all over the place, this build allows you to try and kill that scv earlier. When going 9 pool, you should save up at 9/9 till you get 200 mins, which should turn into a spawning pool. From here, you should build another drone and an overlord soon after, or for those who think their supply will be a bit late by the time the overlord comes out, build an overlord after the pool and follow-up with a drone. As soon as your pool and overlord finishes, make all 3 larvae into zerglings. From here on, it depends on your style. Do you want to go for pressure low economy zerg or pressure into macro zerg?
Low Economy
For those who like to go low economy pressure zerg, after a 9 pool, you will probably continue to add zerglings after your 6 made from the completion of the spawning pool. But even still you should be making a hatchery as soon as you get 300 mins, and you should add gas if going for low econ, as slow zergling even in the beginning, are not too useful as they can be with speed and lair tech units. Even though you are going low economy, don't forget to add drones when you can. Low econ can be deadly is used correctly, but it can also be a self destructing move if you forget to give yourself enough to live on. From here on you can decide on whether you want to go for a muta/ling combo or a lurker/ling combo. Highly suggest you do 2 hatch first, then add a third hatch later.
A. Muta/ling
Constantly keep pressure on your terran opponent, pick off everything you can and try to keep your tech and your economic position secret. Zerg's versatility is what makes them so deadly, and keeping them a secret from your opponent makes it that much better. From here on add drones and lings as needed. Don't forget your second gas and don't forget drones. Keep watch of what he does, and don't try to be a hero and kill his first army that is coming out unless you know for sure that you can take it [firebats are deadlier than you think, dont underestimate 1 or 2 in the army]. Make a couple overlords and save up larvae. Hopefully by this time you will have 1-3 control group of lings and have enough money/gas/supply to make 6 mutas as soon as the spire finishes. From here, expand again and continue to add more mutas. I suggest that you keep adding more to keep them in their base and keep harassing them, but this next part is for those going all-in.
If you are going all in with this, it is better for you to add a third and maybe even a fourth hatch in your base, and continue to make mutas and lings continuously. Don't let your macro slip. But when harassing, more important than picking off worker, is to pick off marines/medics/firebats. Why? Considering terran went for a fast expo, you want to break their front and roll them over with streams of mutas and lings; picking off scvs rather than marines won't be as much of a benefit for you if your trying to steamroll him units. Hope your muta micro is good.
For those who want a fallback, just in case they can't end it with muta/ling, like I said before, expand and continue to add mutas. But instead of continuing to add mutas te entire time, you need to stop and add a hydra den and an evolution chamber. Upgrade lurker and carapace. You need to keep them in their base and get lurkers as fast as you can. Depending on what you saw in their base [ex. did they get drop ship or vessel first?] you should put lurkers at your expo [if you saw a dropship], or in front of their base [if you saw a vessel]. Try to take up as much time as you can and macro up while getting a hive [you should be running off three gas]. Don't forget scourges for those pesky vessels and dropship, and pick them off if you can. This is will put you in a substantial lead, especially if you can get a vessel. Get a defiler mound and upgrade consume as soon as it is done. Don't lose your first units unless you can take it down with little casualties. You need your army for your swarm. A nydus canal to your expo at this point would be nice, especially if the terran decided to go for your expo at this point. Hope your swarm is good. You will need good swarming and consuming to push the terran back. From here on you should continue to take expos and defend them with lurkers/ling/swarm/scourges. But don't let terran take expos on will, you need good scouting to see where his army is, where they are moving, where he is expoing, etc...
Try to swarm into his natural (when you get swarm, this is the point where you should be on the attack), from there you should be able to swarm into his main and eventually take the game. Don't forget to upgrade not only attack/carapace, but also faster attacking for zerglings, faster movement/armor for ultras [if you get to this point], and plague and extra energy for defilers. By the time you get to ultra/swarm/plague/ling/scourge, you will hopefully have an easy time dealing with the terran army, and should be able to take the game. This is only a broad guide.
B. Lurker/Ling
This is where you decide that you want to play it a little safer and get your economy back up. By the time your lair reaches about the midpoint, you should add a hydra den and an evolution chamber (optional). Upgrade the lurker aspect as soon as both the lair and hydra den finish and make some hydras. Here you can decide to get them to your expo or your opponent's natural. I'm going to write the guide as if you sent them to your opponent's natural. Morph the hydras into lurkers as soon as the upgrade finishes and burrow them in front of his natural as soon as they complete. From here on out, just continue to make more lurkers/lings, and add a spire for the scourges to kill dropships and vessels. Stall the terran attack for as long as you can while getting Hive and a defilers mound. Hopefully you haven't forgot to upgrade because at this point, it will matter. I cannot be too specific after this, but all I can say is to watch for drops, don't let him mass vessels, get all the defiler upgrades, be aggressive with swarm, expand, upgrade, and hopefully you'll be able to play your way into a victory.
9 Pool Speedlings
This is a variation to the 9 Pool. Basically what you would do here is make a pool at 9/9, add a drone, make a gas, send three drones to mine gas, wait till you get 88 gas, then send the drones mining gas back to the minerals one by one. You then make 6 zerglings and upgrade speed at the same time. This puts alot of pressure on terrans and forces them to take out scvs. You then have options from here. Are you going all-in, are you going to continue making zerglings and play low-economy, or are you going to change into more economy? Either way, all these choices involve getting an expo. So make a natural expo regardless of what you're doing so that you have a fallback.
