Don't let it scare you! The neat thing about modern cameras is that they can be used just as simply as a P&S camera if you want - just stick it on Auto mode (the green camera icon) or P mode, and point & shoot. Plus, it'll outperform the standard compact P&S cameras because of the larger sensor with better resolution and better high ISO capabilities.
In the meantime, there are plenty of books you'll see recommended around this site (I've never used any, so I won't endorese one)...and even this site itself is a great place to pick up tips. Always feel free to ask about a mode, button, or function you don't understand...someone here can probably help. And check out the Sony Alpha photo thread, where you can get inspiration and a glimpse of some of the wonderful stuff you can get out of your camera as you get to know it and master it.
And with digital - I'd encourage you to play. Take a bunch of pictures in different modes - see what they do. The A330 is better than most in that the camera itself has some excellent help screens, descriptions, and various graphical displays to show you what different modes and functions do...it's really great for folks new to photography or DSLRs to get a little built-in help right on screen.
I've got the ancestor to yours - the A300 - and love it. I'm on about 1 1/4 years and have taken thousands of shots in every conceivable environment and style. All DSLRs are pretty amazing and capable -so much more than compact cameras. You'll find as time goes on that you may start to develop a bit of 'lens lust' for some additional lenses that will increase your capabilities, but for now, with the much improved kit lens your camera came with, you should be able to learn quite a bit about photography...just shoot often, and always ask what you don't know!