StarCraft/Protoss mission 3: Higher Ground

Establishing the base
Following the pattern developed in the previous campaigns, you are allowed to climb just a little bit further up the tech tree in this mission. Specifically, Stargates are available for warp-in this time around, which means you can build Scouts. Before you start building a victory fleet of Scouts, though, you've got some infrastructure to take care of.

Both Zerg bases (there's one directly to the north of your starting position and one in the left side of the map) will airdrop units on your base fairly often, so build a Forge and work on warping in some Photon Cannons, making sure all sides are protected (this includes the ridge to the north). Then build two Gateways—you'll be pumping out units much faster—to make some Zealots. Now you're pretty much set against enemy attacks. Zealots murder Zerglings, Cannons are good against Hydralisks, and the Scouts that you start with will kill enemy Overlords in just a few volleys of their powerful missiles.

Now you can start working towards a strike force. Build a Cybernetics Core to unlock the Dragoons, and start upgrading as well as making units; ideally, you'll have every available upgrade done when this is over, but for now get Singularity Charge (Dragoon range) at the Core and the Shield upgrade at the Forge.

Expanding
This is still pretty early on in the campaign, so you have more than enough resources in your base to beat this mission. However, to make the process of building an army go faster, you can make an expansion base in the bottom left corner of the map and harvest from the large deposits there.

Once you have a sufficient defense of Cannons and units back in the main, take the Scouts and a Probe to the expansion location (see screenshots for clarification). There will be some burrowed Zerglings near the minerals, but you can lure them out of hiding by sending the Probe forward. Then have the Probe run away while the Scouts shoot the Zerglings (repeat until they're all dead).

While the Nexus is warping in, it would be a wise move to set up Pylons and Photon Cannons in a defensive formation. Also, build your Stargate here, and defend this base with reinforcements from the main.