You can edit the color scheme settings file found in data/init/colors.txt. The file is fairly self explanatory - DF uses 16 color different colors, and each of those colors are further split into RGB channels when setting the colors. Before modifying this file, it is a good idea to make a backup of it.
MagmaWiki has a comprehensive list of examples where each color is used, as well as examples of alternative color schemes you can use on the color scheme article.
This is the scheme I'm using:
[BLACK_R:0]
[BLACK_G:0]
[BLACK_B:0]
[BLUE_R:30]
[BLUE_G:85]
[BLUE_B:165]
[GREEN_R:70]
[GREEN_G:125]
[GREEN_B:55]
[CYAN_R:45]
[CYAN_G:145]
[CYAN_B:135]
[RED_R:170]
[RED_G:20]
[RED_B:0]
[MAGENTA_R:130]
[MAGENTA_G:40]
[MAGENTA_B:115]
[BROWN_R:120]
[BROWN_G:80]
[BROWN_B:50]
[LGRAY_R:160]
[LGRAY_G:160]
[LGRAY_B:160]
[DGRAY_R:100]
[DGRAY_G:100]
[DGRAY_B:100]
[LBLUE_R:90]
[LBLUE_G:130]
[LBLUE_B:210]
[LGREEN_R:110]
[LGREEN_G:180]
[LGREEN_B:55]
[LCYAN_R:70]
[LCYAN_G:215]
[LCYAN_B:195]
[LRED_R:215]
[LRED_G:60]
[LRED_B:0]
[LMAGENTA_R:210]
[LMAGENTA_G:85]
[LMAGENTA_B:190]
[YELLOW_R:235]
[YELLOW_G:180]
[YELLOW_B:0]
[WHITE_R:250]
[WHITE_G:250]
[WHITE_B:250]
