<p>Is there an intuitive way, or a good mnemonic, for understanding the correspondence between colors and their hexadecimal values?</p>

Hexadecimal colours are of the form #RRGGBB where RR is red, GG is green and BB is blue. Since they're hexadecimal they range from 00-FF. It should be fairly easy from that to gauge roughly what kind of colour you're dealing with for example #FF12A3 is going to be fairly red.