The way I got better at web design is just practicing. Every time I go to a site that looks really nice, I kind of store the ideas back in my head. And evventually, all of the ideas that I've seen come together in something that's presentable.
I don't think Flash is a requirement. I want to learn it and it may become one of my projects over the summer when I have time - make a Flash-driven website.
As far as color schemes, it's whatever you think looks good together. I usually tend to put like colors alike. For example, a dark grey background with light grey or white text on it, etc. Just try and keep all the links (visited, unvisited, active, hover, etc.) and graphics all within the same general color scheme. Another idea that's really kind of corny, but not a bad one is this (I've done it before and it does actually work): go to Kmart or some other store with a paint department that has paint swatches that you can take home with you. As dumb as it may sound, try and go to Kmart because they have the Martha Stewart paint there (I used to work in the hardware department at a Kmart, so I know). She takes colors that she thinks looks good together (like 4 of them) and puts them on one paint swatch. Just find a few that you like and take them with you and try and use those color schemes (either scan the colors in for a close match or just eyeball them). That's what I do, anyway, and as crazy as it sounds, it does actually work.
That's about it, really. Just practice and keep your eyes open. Look at magazines, etc. for other inspiration. Anyway, back to packing up all my stuff to go home for the summer and studying for my last exam. PM me if you got totally lost in what I said.