Why?
In the digital world, colors are most commonly represented as addition of three primary colors Red, Green and Blue (RGB). Each component of Red, Green and Blue can have a value between 0 to 255. 0 being the least amount of that color and 255 being the most amount of that color. So a color can be specified by defining how much of each primary component it possesses. For eg, Black is defined as R=0, B=0 and G=0 the absence of all colors.
The reason we need color management is that when we specify a color by the 3 RGB values and send those color values to two different devices, the output from those devices will be different! What is needed is the ability to know how each device will respond to the RGB values and then feed different RGB values to the devices to make them produce the same color. The process of doing this is Color Management. Why is this important to Photographers? Because it is crucial to ensure the images/colors that you capture are reproduced exactly when they are printed, displayed etc.

The 3 RGB values together will give us the possibilility of having 16 million colors possible. However, most hardware devices that actually produce color i.e scanners, printers, cameras, monitors etc are capable of only displaying a small subset of all the possible colors. This subset varies from vendor to vendor and product to product. This subset is called “Gamut” or the Device’s color space. So colors that are outside the device’s ability are called “Out of Gamut”. There are lots of technical reasons why each device cannot be made to have the same Gamut. Suffice to say, if it were possible, there would be no requirement for color management. It is not possible.
Now when most devices produce color, they produce RGB values that have meaning only in their color space. A pixel that is red in color (R=240) sent to one monitor will produce a deep red, another a light red. if we knew that the original red is actually tomato red we would send R=225) for monitor A and R=245 for monitor B. This will produce tomato red in both monitors. So a RGB vaue has meaning only if it is relative to the device’s color space.
This relative color space is characterized by the color profile of that device. So color profiles are nothing but a description of the boundaries of the colors that possible within the absolute color space. Once we have the profile it is possible to convert the RGB numbers from the original pixel to the right RGB numbers required for that monitor’s color space.
To help work with transforming from one device color space to another, there are several indutry wide color spaces that have been standardized. One is Adobe RGB and the other is sRGB. sRGB has much smaller gamut than Adobe RGB. But sRGB is used as the defacto standard for viewing documents on the web and on a typical computer monitor. Adobe RGB is useful for printing.

To enjoy the best of both worlds, it is best to use AdobeRGB as much as possible as our color space and then finally do a conversion into sRGB at the end before using it for viewing or in the Web. (read more)
How?
How does one color manage? First step is to calibrate your monitor. By default, the monitor is assumed to be having a sRGB profile. However, this is only an approximation and a bad one at that.
To manage the color correctly, you need to create an accurate profile for every device you work with. The most important one is your monitor. This can be done by software or hardware. Hardware is more accurate but much more expensive. You can get reasonable results using software. I use Adobe Gamma that ships with Photoshop 7. Run adobe Gamma from the windows control panel and follow the procedure. At the end it will create a profile for your monitor and saves it as your profile for your system. Now essentially a color profile (.icc) has been created for your monitor.
When you use a color aware application like Photoshop, it will look at the display’s profile and then convert the image’s data so that you see accurate colors as the original looked like. If you did not have this step, the colors would be just converted assuming a sRGB space.
Now when it is time to Print, you want to know the Printer’s color profile. Many professional photo labs will supply with you one (link to drycreekphoto). I use Adorama’s printing service and get good results. It is possible to preview how the images would look when converted to that profile by soft proofing in Photoshop. If the image doesnt look right, adjustments can be done to the image to make it match the colors you want. So even before a real print is done, it is possible to ensure that you will get the colors you expect.
What other decisions to make? You need to use one standard color space (sRGB or AdobeRGB) for editing images. You should not use any device’s color space for editing. AdobeRGB is preferred because of its wider gamut. The workflow is to import images into a color aware application and then convert them to a working color profile (like AdobeRGB), either Adobe RGB or sRGB. Once it is worked on, change the profile to be sRGB if they are going to the Web or to a printers profile if they are going to be printed. Finally remember, viewing an image’s true colors can only be done via an application viewer that knows how to do color management. Viewers like the inbuilt in viewer in Windows XP are not color managed.
You are now on your way to becoming Color Managed!
Note: If you are feeling adventurous, a good place to dive into the world of color management is Norman Koren’s website. It goes into too much detail without giving an overview in my opinion. But with the general principles above, you should be able to understand the nitty gritty details easily.
