The Theme Customization API, added in WordPress 3.4, allows developers to customize WordPress’s Theme Customization admin screen. The Theme Customization screen (i.e. “Theme Customizer”) allows site admins to tweak a theme’s settings and see a preview of those changes in real time.

To add your own options to the theme customizer, you need to use a minimum of 2 hooks:

customize_register
This hook allows you define new Theme Customizer sections, settings, and controls.

wp_head
This hook allows you to output custom-generated CSS so that your changes show up correctly on the live website.

customize_register
This hook allows you define new Theme Customizer sections, settings, and controls.

The ‘customize_register’ action hook is used to customize and manipulate the Theme Customization admin screen introduced in WordPress Version 3.4. This hook is a component of the Theme Customization API.

function mytheme_customize_register( $wp_customize )
{
//All our sections, settings, and controls will be added here
}
add_action( 'customize_register', 'mytheme_customize_register

This hook gives you access to the $wp_customize object, which is an instance of the WP_Customize_Manager class. It is this class object that controls the Theme Customizer screen.

Generally, there are only 4 methods of the $wp_customize object that you will need to interact with inside the customize_register hook.

WP_Customize_Manager->add_setting() This adds a new setting to the database.
WP_Customize_Manager->add_section() This adds a new section (i.e. category/group) to the Theme Customizer page.
WP_Customize_Manager->add_control() This creates an HTML control that admins
can use to change settings. This is also where you choose a section for the control to appear in.
WP_Customize_Manager->get_setting() This can be used to fetch any existing setting, in the event you need to modify something (like one of WordPress’s default settings).

wordpress theme api