Here is a great tutorial on how to add a colorpicker to your admin page.
Regardless of how you are adding a colorbox or what plugin you are using, assuming you added it by adding a field in your options table (as provided in the link), you can use the color value anywhere in your template files with a call to get_option
:
$options = get_option( 'my-theme-options' );
$bg = $options['background'];
For example, as mentioned here, to colorize your first level headings add the call in your wp_head
section.
function my_wp_head() {
$options = get_option( 'my-theme-options' );
$color = $options['color'];
echo "<style> h1 { color: $color; } </style>";
}
add_action( 'wp_head', 'my_wp_head' );
Make sure you validate and escape appropriately when handling user inputs.