Zerg players tend to take an early third base agaisnt the protoss forge fast expand in order to edge out an economic lead agaisnt one of the most economical builds protoss has in their arsenal. This build is based around the strength of +1 zealots against non-upgraded zerglings which die in two zealot attacks rather than one.
This build is a continuation on the basic forge fast expand build v Zerg which can be found here.
19 – Assimilator x2
Build two zealots, then two sentries. The zealots are for early scouting, the sentries for defense
Construct a proxy pylon near the zerg’s eventual (or current) third base
100 Gas – +1 Ground Weapons
24 – Cybernetics Core
6:45 – Gateway x3
8:00 – Zealot x4
Pressure the third base with up to three rounds of zealot warp-ins
Retreat if large Roach numbers arrive, continue the attack if there are only zerglings, queens and/or spine crawlers. It is usually worth it to sacrifice your attacking zealots to kill your opponent's third hatchery.
From here hopefully you have done reasonable economic damage to your opponent or killed their third hatchery. You can now fall back and defend any counter-attacks using sentry force fields and other units. You can now transition into colossi, immortals and blink stalkers or another composition to deal with your opponent's composition.