Depending on how far you want to take it, I think it's very important to study Design before studying Web Design. Learn the principles of good design - the rule of thirds, color theory, negative space, typography, etc. - then apply that to the web. One wouldn't study open-heart surgery without first going to medical school. That analogy may be a little dramatic, but I hope you get my point.
Not to totally discount gigawatt's advice, but I've watched many a graphic designer fail miserably at web design. Be wary of trying to apply print principles online, in particular.
I agree and would go even further - most designers that start out as graphic designers are doomed to fail as web designers and I've rarely seen any that made the transition completely. The high profile people making high bandwidth flashturbation for movies, rock bands or new vodka brands don't count - just because an ad agency can sell it to a big corporate client doesn't mean that's what the website's visitors will enjoy or be able to use easily.
Web design is not graphic design. It's not a subset of it, not even a sibling design branch and if anything, it's a distant cousin. Making stuff for the web is much closer to industrial/product design and architecture than anything in the communication arts. It's a different matter to design things simply to look good than it is to design how they work.
So then how would you learn fundamental design principles without getting polluted by the biases of print design? The best answers below are a bit dispersed (too many pointers to the css/html/js skills you said you already know) so I'll distill: 1) learn only the core graphic design principles - see endlessvoid94's book recommendation. 2) I second PStamatiou's advice to get your own site and start tinkering with it immediately, preferably a blog. Can't stress this second tip enough, actually.
Good point, wmeredith. The principles do apply to both, though. When I've seen print designers fail, it's been when they try to force the web to behave like a magazine or a book. Seems like the author is already accomplished at building websites, so he probably has a good idea of what works and what doesn't.
