You can actually become a skilled designer in part by simply browsing the Web and understanding how you use it. If you know how people use the Web, you can design for the Web. There is a sixth-sense of sorts that comes along with “pleasing the eye,” but usability is the most important part. You can get far by studying the fundamentals of design (line, shape, color, contrast, et. al.) but I believe some people, by nature, tend to create things that instantly appeal to greater masses.
Also, I think every designer starts out by copying what’s been done. There’s nothing wrong with copying things, especially good things, but there’s a common sense line that you wouldn’t want to cross.
And finally, don’t think about Web design in terms of CSS or HTML or Hexadecimal color values. Sketch and scribble out ideas first, use crayons and colored pencils, etc. Start off the computer first, then either refine your ideas in Photoshop or Fireworks, or jump right into HTML/CSS. One thing I do sometimes is try to prophecy the final design by just closing my eyes and letting something pop into the black void. Sometimes I see something instantly and it works out, other times I need to engage my brain more either through research/mental exercise or even physical exercise. Never ignore an idea, no matter how bad it seems. (Now I’m just rambling…)