How to update user profile custom fields

I use update_user_meta to update the fields. You can add this in functions.php of your child theme.

function save_extra_user_profile_fields( $user_id ) {

if ( !current_user_can( 'edit_user', $user_id ) ) { 
    return false; 
}

update_user_meta( $user_id, 'telephone', $_POST['telephone'] );   
}
add_action( 'personal_options_update', 'save_extra_user_profile_fields' );
add_action( 'edit_user_profile_update', 'save_extra_user_profile_fields' );