The hook wp_ajax_{action} is for logged-in users and wp_ajax_nopriv_{action}
for non logged-in users.
For example in your functions.php file,
add_action( 'wp_ajax_your_ajax_action', 'your_ajax_function_callback' ); // logged-in users
add_action( 'wp_ajax_nopriv_your_ajax_action', 'your_ajax_function_callback' ); // logged-out users
function your_ajax_function_callback() {
// handle ajax request
}