Always start out slow and progressively become faster and find the limits of your car and tires. Second, I would suggest to have someone who's fairly experienced ride with you to give some pointers and techniques. Third, do what Ravage just said - practice. Like all things in life, that's about the only way to get better.
As far as learning proper braking points, turn-in points, and different techniques for different corners and obstacles, the best suggestion I can make if you don't have the means (say a nice road where you can safely learn to drive through a corner), pick up a game like Gran Turismo 3 or 4 for the Playstation 2 and go through the license tests. Commence laughing at me now, but it's a great way to learn driving techniques from different corners - like slaloms, esses, and hairpins.
As far as shifting and the clutch, be nice to your clutch. If you're just looking in getting into autocross, most courses only require you to shift from first to second. You'll spend the remainder of the course in second gear, so there's not much shifting technique involved. Also, they have a short roll out before you trigger the timer for your autocross run, so there's no need to be abusive on the clutch.
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formerly known as the member ilcowil