There are basically two build orders for zerg in starcraft 2 coming out of the beta. There are sure to be a lot more coming in the next few months and years as Blizz continues to tinker with balance, but as of now, these two builds are what you will see from power players. The first one is the one base build, and the other is the fast expand. the fast expand is the most used version since zerglings make such a great unit in the first part of the game. They can give you an advantage that is hard to recover from if you can get enough of them right out of the box.
The one base goes like this: Drone, Drone, Drone - 10 supply -> Overlord, Drone, Drone, Drone - 12 supply -> Spawning pool, Drone, Drone, Extractor, Drone, Drone, Overlord, Spawning pool finished -> Queen
For fast expand you will do: Drone, Drone, Drone - 10 Supply -> Overlord, Drone, Drone, Drone, 14 supply -> Spawning Pool, Drone, Drone -> Extractor, 15 supply -> hatchery at base 1, Drone, Drone, Overlord, 18 supply -> Queen,
You can also go for a 6 pool build but it is rather risky. Instead of worrying about anything else, you spend all of your initial resources and time getting a spawning pool from a single drone - it goes like this: Drone, 200 minerals -> Spawning Pool, Drone, Drone, Spawning pool finished -> Zergling X3.
You are going to get attack units in the form of zerglings faster than anything else and can get into his base and start attacking before he can even get a single building built. But unless you can kill off five or six of his workers your economy may never recover from going short handed with drones yourself.
After the standard openers there are two basic strategies you can use. The first one is Zergling/Mutalisk, and the second is Roach/Hydra. the first type works best with the fast expand opener with a few zerglings and a spine crawler or two to beat off early attacks. Get the speed upgrade for zerglings with your second 100 gas, and use the first 100 on the lair upgrade. Once you're done with those two items spend everything you've got getting the spire upgrade and then past that it all goes into Mutalisk creation. Once you get five or six Mutas you can go to work killing off workers. Make sure you don't get any of them killed while you get more zerglings for a full frontal attack. This strategy devastates your opponents economy and makes it very unlikely they will ever recover while you run up more and more fast zerglings to take out whatever they can manage to build.
The roach/hydra build doesn't rely on a fast expand. Defend your natural base and send some zerglings out for early pressure. Get a nydus worm in a good spot and continue to harass while you build up a good force of roaches and hydras to make the killing blow. Use an Overlord to give you vision of the back side of his base and then just pop out through the worm in a surprise spot and catch them off guard and out of position.
You can always choose to mass just about any unit as Zerg and overwhelm with sheer numbers. The best units to use for this are Mutalisks and Hydralisks, but even zerglings can work if you can get enough of them in the right place at the right time. We don't have the time to go into all of the specific strategies for the zerg in this article, but the two standard openers combined with the two basic following builds will work nicely most of the time.
