Here's how to 6 zergling rush in under 3 minutes, and also have money.

-Build 1 drone, and put the 4 on minerals. Scout with your Overlord.
-When the drone is ready, put him on minerals.
-When you have 150 minerals, build a spawning pool.
-While it is morphing, build 2 more drones. Note: Do not wait for 100 minerals, and build 2 drones at the same time. Build 1 right when you have 50 minerals, and build the other when you get another 50 minerals.
-When the pool is done, you should have 150 minerals and 3 Larva. Make them Zerglings.
-While the Zerglings are morphing, a Larva will pop out. Morph him into an Overlord.
-When Zerglings are done, rush your opponent, and he should be eliminated.
-If for some weird reason he's not, you still got some money to build stuff.