Make a web page and iterate your design. Go through about 10 cycles of "read stuff about design" and "re-design". Then try another type of website. Different types of sites have different goals. There are business, blog, news, social networking, etc...

Software: I recommend Inkscape for drawing logos, Gimp for manipulating images. Photoshop is much better than either of them if you have the $$$.

Edit: Whoops, meant to reply to the parent thread.