Before we begin
So, before you actually go ahead and start with the calibration process, there are a few things you should do to get the most out of the process. First, make sure that there is no glare on the computer screen, or any complex patterns or bright colors reflecting on its surface. You want as little interference from ambient light as possible, especially in your usual workplace.
Then, make sure that the screen is set to the highest resolution possible, and that the computer is in high color mode. While this may vary by distro somewhat, this will most likely be found under some variation of “Display Preferences." In Ubuntu, for instance, this is found under System => Preferences => Display Preferences.
If you're using a monitor that is separate from the rest of the computer, there may be a way by which you can adjust these settings via dials and buttons, as opposed to using some sort of frontend software. This certainly makes the process easier, so see if this is an option before you begin.
Also keep in mind that the manufacturer often provides a default color profile for use with the product. While the color profile will of course change over time with age, this may be a good starting point.
It should also be noted that Linux distros were not exactly designed for this sort of attention to color management, so the tools available are not optimum. There is no central user control panel for color settings, so separate programs have to be downloaded and learned, amongst other issues.
Now, the remainder of the article will cover various methods by which one can calibrate the monitor. These methods can either be used in combination, or independently from each other.