Playing as a Zerg against a Protoss opponent can be a huge challenge as the Protoss has the ability to construct the ultimate counter units to whatever Zergs may use to attack them.
For the Zerglings, they have Zealots and Colossus.
If we go for Roaches, they can crush them with ease using Immortals.
As for the Hydralisks, the Protoss will counter with Stalkers and Colossus.
Whatever a Zerg player may attempt, the Protoss has the perfect reply to it at the tips of his fingers.
This begs the question: What Starcraft 2 strategies must a Zerg employ to win against a Protoss enemy? The answer to that is by simply out-gathering and out-producing him.
This Starcraft 2 strategy guide will instruct you on how to defeat a Protoss player using a starvation technique.
The key to this Starcraft 2 strategy is to go for expansion early on in the game and restricting the enemy's expansion.
At the beginning of the game, construct a bunch of Zerglings to keep the opponent occupied so that his focus is not towards expansion.
Now, skip the Lair upgrade and use the Minerals you have to expand.
Since you have delayed the Lair upgrade, you will be extremely vulnerable to aerial attacks, so make sure the opponent is not gunning for a Void rush.
After your expansion is complete, switch over to Hydralisks and build up an army.
I would also suggest creating some Corruptors to use against Colossus and Void Rays.
Always make sure to keep the Protoss player from expanding and wait for his assault, do NOT attack him first.
Soon enough, he will run out of Minerals and will have no choice but to launch an attack on you.
At this point, you should have no trouble in defeating him as you have two bases whereas he only has one.