I recommend you start by reading up on computational color theory. Wikipedia is actually a fine place to educate yourself on the subject. Try looking up a color by name on Wikipedia. You will find more than you expect. Branch out from there until you've got a synopsis of the field.
As you develop your analytic eye, focus on understanding your favorite (or most despised) interface colors and palettes in terms of their various representations in different colorspaces: RGB, HSB, HSL. Keep Photoshop/GIMP open so you can match the subjective experience of palettes to their quantifiable aspects. See how your colors render on lousy monitors. Notice what always remains readable, and which color combos tend to yield uncharismatic or illegible results. Pay attention to the emotional information conveyed by specific palettes. You will quickly see patterns emerge. For example, you will realize that high saturation colors are best avoided in UI components except for special purposes.
Eventually, you'll be able to analyze the output of the palette generators recommended here, and you'll develop your own theories about what makes a good match, and how much contrast is needed to play well on most displays.
(To avoid potential frustration, you might want to skip over to Pantone's free color perception test. It's best taken on a color calibrated display. If it says you have poor color perception, then numeric analysis is extra important for you.)