One of the trickiest things to recognize about working in digital art is whether you are working in the color you see on the screen. Ideally all computer monitors would work the same way, displaying the same color given the same signals from the computer. In the real world monitors vary slightly in how they reproduce the colors. This means that you may think you're working with a nice shade of pink or whatnot, while the color that's actually going into the image you're painting is much redder than you think. Then what could be worse is if the workflow in your office has the image go from graphics artist to graphics artist, all of whom have different monitors, each of which are rendering the colors slightly differently. They may each "touch up" the image, but because their monitors are slightly different end up totally screwing up the image.
What's better is to calibrate your monitor. Monitor calibration means to ensure that the color on the screen is pretty darned accurate given the signals coming out of the computer.
Some operating systems come with built in utilities to help calibrate the colors. On the Mac OS X system (what I'm familiar with) the system control panels include a Calibrate feature which lets you tune the color settings exactly for your monitor. Included in the calibration is some splotches of red, green and blue which let you adjust the redness, blueness and greeness of your monitor.
However, you can do better than this through purchasing add-on software and hardware.
Pantone Colorvision Spyder with Photocal: Hardware and software that runs on both Windows and Macintosh computers. The hardware straps to the front of the computer monitor and digitizes the color the monitor is actually displaying. This lets the software precisely control the color, much more than you can with your naked eye.
Pantone Colorvision Spyder Photo Suite Pro: As above but with some extra juju for printers.
PANTONE COLORVISION SPYDER PRO WITH PRINTFIX: As above but with other juju for printers.
Color Confidence: The Digital Photographer's Guide to Color Management by Tim Grey: Color Confidence is a results-oriented guide to managing color effectively across all devices. In his approachable style, Tim Grey demystifies the complicated topics and leads you step-by-step through each component of a color-managed workflow. Designed for busy photographers, this full-color guide cuts through the theory, focusing on the practical information you need to make the best color decisions from capture to output.