Use the keyboard commands. Ordering your units around with the mouse is slow. Each command has a keyboard shortcut, such as A for Attack and B for Build. Get used to the keyboard commands, and your army will feel like a well-oiled machine.

Build lots of first-tier combat units. New players often try to build up their tech tree as quickly as possible because they want the big flashy stuff--and just as often lose to a guy who builds a handful of cheap attack units and attacks early. Think of it this way: you have to earn those big flashy units by living long enough to get them without losing, and for that you need Zerglings/Zealots/Marines.