An effective cheese for zerg, especially against A.I. is making hatcheries as fast as possible, build one as soon as your mining is faster than you can breed with, make the spawning pool asap while the hatchery is going.
Try making an overlord first, or at least a drone and then an overlord.
Rush your zerg as soon as you have 10 and breed more from both hatcheries.
In the start you never want to be making more armies than drones, its easy to go overboard and neglect resources when you need it most, keep armies to a minimum, dont build much static defence unless they support your forces.
Evolution chamber: has to be ready when you have some vespene gas to spend, no sooner.
Once you can make roaches, make some roaches and build a lair, from there you should have 4 hatcheries and be making a spire and a hydralisk den at the same time, from there its an open (but late game) if you have survived this long as zerg you have wave after wave of zerg appearing.
Look at earlier parts of this series for tips on management to get your speed up for this process.