Playing the campaign will only teach you the very basics of the game (i.e. how to build a unit). Beyond that, you'll need to look at some guides. The ones I suggest are the stickied thread above this post, and some general Zerg tips here, with some race-specific strategies: http://www.teamliquid.net/forum/viewmessage.php?topic_id=73314
Also, get to know the other races' units and strategies as well. That way you'd be prepared to counter them as you'll know what's coming. Good luck.
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