Beginner Tips & Strategies

Bring Along The Dropships Etc.
Don't leave home without at least a Dropship, Overlord, or Shuttle filled with SCVs, Drones, or Probes. If you are attacked and have no way out, these peons will enable you to start a new base.

Keep Mining for Vespene Gas.
Vespene gas is never truly depleted. When the game informs you the mine is depleted, it's lying to you. What's really happening is that your worker units can now only carry two units of Vespene instead of the full eight in each trip. You are much better off reassigning the units to untapped Vespene geysers, but it's nice to know that no Vespene mine is ever completely empty.

Better Mining.
When harvesting minerals, remember that only one mining unit can access each cluster of minerals at a time. Sending all of your units to the exact same mineral location (square) can cause delays as each mining unit waits for access to that location. To speed things up, assign each mining unit to a different square.

Use Detector Units
Don't underestimate the value of Detector units (like science vessels, overlords, or observers). They can spell the difference between conquest and carnage when you're being assaulted by hoards of invisible attackers.