In the beginning of the game i make alot of drones then build a spawning pool then build another base near my main base then build zerglings, roaches, and air units. I evolve my hatchery into lair then build an overseer.
Yeah from what I've heard Zerg usually expand early on. A good thing to do is get some Zerglings out earlier too and try to rush and harrass your opponents mineral line.
You are going to want some sort of army before you expand so you will be able to defend yourself or start putting pressure on your opponent to prevent them from being very aggressive.