If you're looking for easy with a fast kill, the Zergling rush is an effective strategy
. The adaptation I'm going to outline here is more useful than the wimpy rushes you may have seen before.
The key is to see strategy as using your strengths against your enemies weaknesses.
Do you remember the story of David and Goliath? Goliath was a huge strong, drugged up psycho. David was small and physically weaker. His chances of making it out alive 1 to 1 bare knuckle, toe to toe, were slim to none. That's why he used a sling shot. He kept out of range of Goliaths sword and brought speed and leverage to put him down.(Bible stories had to be of use to me sometime!)
So only use this against either Zerg or Protoss and not against a Terran.Terran gamers can easily build a wall around their base, stopping your zerglings in their tracks.
Get going by using your starting drones to harvest minerals. The real key is to start with 6 drones. Keep it at that and save up 200 minerals. Then you can build a spawning pool. Build two more drones as the spawning pool is developing. Let the new drones save 150 minerals and when the spawning pool is ready get 6 zerglins.
Right after that make one gas with a drone, then build another zergling. Then you make another gas and build 2 more zerglings. {From here you can stop both gases and attack with ten zerglings instead of just six. Bigger numbers means a more powerful and effective strategy.
Another variation is to produce a Queen from your spawning pool. Build the spawning pool at 9 of 10 supplies. This is essential! The Queen allows you to easily produce more Zerglings with its Spawn larva ability. So instead of one rush of zerglings you can send in two waves. As each larva gives birth make another 12 zerglings. And if you can boost the speed with a speed upgrade for the Zerglings even better.Speed is your ally in this attack. Speed doesn't just stun, it criplpes and kills.
Just remember only use this against other Zerg or protoss opponents.It's too weak against the Terran!