The Zerg are very flexible having the ability to produce any unit from a hatchery.
Our first unit is the zergling. There are a few things you can try early on with them. One is the simple 6 zergling rush, which is deadly to any unprepared player who happens to very close to you. This will make up for the poor economy that you will have. Zerglings lose against masses of marines. So try not to use them too often against a terran player who has had enough time to create a dozen or so marines. Zerglings fair about even with zealots, however you must know that it takes 4 zerglings to kill one zealot, so make sure you can estimate your battles properly.
The sunken colony allows a Zerg player to take an expansion early with good defense from the basic units. So a power up strategy, on maps with a second base, is usually preferable. As long as the chances that your opponent can find you or even reach you is high, then you should take advantage of the 300 mineral base, and the power of 4-5 sunken colonies. This type of strategy, leads to power mutalisks, or hydraslisks.
Hydralisks are a deadly, except that you need groups of more than a dozen to be effective. Lurkers would be a good idea if you have no expansion. This is because lurkers can buy you time, and prevent any land army from advancing past the lurker. So if you need to get expansions, get lurkers placed around your opponents base, to prevent him from expanding and advancing. If your opponent has no detection then run a lurker into his mineral line and the game is over.
Burrow is a great upgrade that many players should use. The best use is to keep tabs on all the expansions, with zerglings, and you'll be able to control the map. Which is an effective winning strategy, since you can take away any expansion your opponent gets.
Burrowing an army of hydralisks outside of base is also another way to contain a player. Wait for them to advance out of their base, then attack his undefended main base. This will cause him to pull back, however you'll probably be able to good amount of workers before he manages to kill you.
Using dark swarm to break into heavily bunkered/cannoned bases is a way to save on losses. Either use hydralisks, which you can cast the darkswarm on top of, or zerglings, where you have to cast darkswarm on the bunkers/cannons.
If you manage to get your hands on an infested command center, use infested terrans to burrow next to every expansion, and have them attack any town hall that gets constructed. Your opponent will lose their 400 minerals, since the infested terran will destroy the structure.
