Here are the things that helped me:
a) read as much as possible on graphic design. The non-designers design book is a great choice. But there are tons of articles across the web on fonts, spacing, coloring, contrast, etc.
b) pick out sites that you like (and that people with design sense like), and practice copying them exactly. If there is some button or styling you do not know how to reproduce, find a photo shop tutorial for how to reproduce it. As you do this, you build up a toolbox of great design techniques. Gradually as you get better and learn how to make pretty sites, your old designs will become embarrassingly deficient to your eye.
c) as you make sites try to solicit detailed feedback from people who know how to design.
Here are some thoughts on specifically why I think your pages do not look so hot:
For your home page: http://www.welton.it/davidw/
The text in your logo needs to be anti-aliased, the edges look jagged. The alignment and spacing of the menu links are off (the horizontal distance is not consistent). Again the text is not anti-aliased so it looks jagged. The spacing between the headers and the text feels off, the header should be closer to the paragraph it represents, not the paragraph above. The top of your bio pic is not aligned with the top of the paragraph. Finally, as a general point try and avoid pure black (#000) on pure white (#FFF). Using slightly grayer font ( #555) softens the page considerably. Also, don't use the default blue for links, use a better looking color. The Adwords look very tacky.
For Dedasys: http://www.dedasys.com/
Again, anti-alias the logo. Try being creative with the font too, maybe download a font set and try making the logo with a more unique font. Alignment of the menu items looks off, centering them does not work. The bullet points should be aligned left. Even better, use a custom designed bullet point rather than the browser default. The colors for the page overall are terrible. To get good colors, I often download a really nature picture, then use the eye dropper to pick out a couple colors. Doesn't always work, but can be quite useful.
Overall, great design is not about being glamorous versus simple spare. Its about getting all the little details right. The balance, color, alignment, etc. And it's about adding that extra little touch in a lot of places - the custom icon for bullet points, the creative logo.
Getting good just requires a loop of reading/study, practice, and getting feedback.