A few things that helped me when I was first getting started:
-Join every web site you can. If there's an interface to use, use it. Social networks, social news, blogging platforms, commerce apps... everything.
-If you don't have a good memory, take notes. Write down the things that stand out to you, even if it's not optimal. Write down the things that are so optimal they stand out. Mark down user interface, design choices. Look at how sites do things. Look at how they handle images and typography and white space.
-As you do that, read things like Smashing Magazine and A List Apart. The most important thing is for you to learn to disagree with stuff you read if you think it's wrong. Sometimes you'll disagree with good advice, and in learning why they're giving that advice you'll learn even more. Sometimes you'll agree with something but other people will disagree, and you'll learn from them.
It takes a long time to integrate what you've learned rather than to make impulsive decisions based on the last things you've seen. That said, there's nothing to stop you from submitting ideas here or to IRC or emailing people for advice, and iterating.
Going based on the terms that you specified yourself:
Clean you get by removing the stuff that doesn't matter. Pare down your features to the bare essentials. If you still have a lot, the challenge is making it so that that lot doesn't seem like much to the end user. If something isn't instantly understandable to somebody that wants it, it can be come better.
Fast is partly a matter of code. In terms of fast interface, clean helps a lot. Big helps, too, but big is relative. (If you only have one button, make it huge. If you have a hundred of them, fast means making it as obvious as possible where the user wants to go.)
Beautiful is the hardest. The one thing that can be said about beautiful is that once you have it, you'll know, and with any luck it'll excite you and make you want to skip around a room. Then, if you look at it a week later and still want to skip, you've got a keeper. (It helps if it makes other people skippers too.)
I don't know about a specific book. Chris Crawford's The Art of Interactive Design is pretty good, but it's expensive. Tufte is great for any sort of related subject, even if he doesn't focus too much on aesthetic.
Here are a few things that've inspired me. Facebook: look at how much they pack into such a compact interface, and how they vary the look of their pages. Tumblr: it's getting worse every year, but the registration experience is pretty amazing, and most of the default blog themes are great instances if you've never seen Tumblr's blog themes before. Both Flickr and Hunch.com - Hunch is one of the most beautiful new sites I've ever seen; the attention to detail is incredible. Hacker News, if you want an instance of how not to waste an inch of space. Last.fm. It's cliched to say 37signals, but 37signals and all their apps. The sites of indie Mac developers very often - I was stunned the first time I saw culturedcode.com, literally* stunned.
Just get into as much as possible and learn what stuff you fall in love with. The fastest shortcut to becoming a great designer is to fall in love hard and fast.
*I MEAN literally, as in: I stared blankly at the screen for a handful of seconds and found it hard to breathe. Yes, I know this is an overreaction, but it happened and I've got no reason to be honest about it.