PatternTap [1] and website design galleries like SiteInspire [2] are invaluable resources for realizing what it is that you like and trying make sense of the design patterns and elements. Dribbble [3] is a great resource too, but you can be easily overwhelmed by it.
So basically just sit down and start looking at other people's work. Analyze why this subjectively looks better that that and you will see the patterns emerge, e.g. generous spacing works really well, and so does contrast, slight texturing goes a long way in certain cases, etc. This will lay a groundwork for general feeling of the design.
Some time after start learning tools (like InkScape, PS or Illustrator) and start reproducing other people's work. This will develop motor design skills. Accenting, nuancing, coloring, pixel-level effects, etc.
I find learning by example a far better approach than going to the classes where you are presented with an already digested version of information; and not shown how best practices compare to not so best practices. Some formal design tutoring is certainly helpful, and it can be done with books and reference materials on as needed basis. This is especially true for composition and typography.
[0] http://dribbble.com/apankrat [1] http://patterntap.com [2] http://siteinspire.net [3] http://dribbble.com
(edit) And no designer is "born with it". They just don't show you their early (crappy) designs, that's all :)
So, I also suggest my own book, which comes out in September, and will hopefully provide such a framework for programmers learning to design: http://designforhackers.com
Take a studio art course. It will require a high level of commitment which is the only way to learn design.
[edit] It also has the potential to make your resume stand out among a stack of recent CS grads.
Learning programs such as Photoshop and Inkscape, IMO, is the easy part. There are so many tutorials about how to do specific effects. But not about when to apply which design principle and such.