Instructions
Go to the forum of your desired game and read the terms and conditions to make sure that having a colored gamertag is permitted.
Look through other players' gamertags in the forum to make sure your desired name is not already taken. Consider using a variation of the name you originally wanted by employing an alternate spelling or adding numbers to your gamertag.
Add the "^" symbol followed by the corresponding color code at the end of your name. The color codes are as follows: 1 for red, 2 for green, 3 for yellow, 4 for blue, 5 for baby blue, 6 for pink, 7 for white, 9 for grey and 0 for black. Your gamertag will appear in the color you select.