wp_insert_user – how to send verification email before logging in

1. Insert user data into wp_users table. Create a page called “Activation” or similar to it and get the ID of that page. An activation email will be sent with the activation link to the user.

function new_user($data) {

    // Separate Data
    $default_newuser = array(
        'user_pass' =>  wp_hash_password( $data['user_pass']),
        'user_login' => $data['user_login'],
        'user_email' => $data['user_email'],
        'first_name' => $data['first_name'],
        'last_name' => $data['last_name'],
        'role' => 'pending'
    );

    $user_id = wp_insert_user($default_newuser);
    if ( $user_id && !is_wp_error( $user_id ) ) {
        $code = sha1( $user_id . time() );
        $activation_link = add_query_arg( array( 'key' => $code, 'user' => $user_id ), get_permalink( /* YOUR ACTIVATION PAGE ID HERE */ ));
        add_user_meta( $user_id, 'has_to_be_activated', $code, true );
        wp_mail( $data['user_email'], 'ACTIVATION SUBJECT', 'HERE IS YOUR ACTIVATION LINK: ' . $activation_link );
    }
}

2. Check activation status while logging in:

// override core function
if ( !function_exists('wp_authenticate') ) :
function wp_authenticate($username, $password) {
    $username = sanitize_user($username);
    $password = trim($password);

    $user = apply_filters('authenticate', null, $username, $password);

    if ( $user == null ) {
        // TODO what should the error message be? (Or would these even happen?)
        // Only needed if all authentication handlers fail to return anything.
        $user = new WP_Error('authentication_failed', __('<strong>ERROR</strong>: Invalid username or incorrect password.'));
    } elseif ( get_user_meta( $user->ID, 'has_to_be_activated', true ) != false ) {
        $user = new WP_Error('activation_failed', __('<strong>ERROR</strong>: User is not activated.'));
    }

    $ignore_codes = array('empty_username', 'empty_password');

    if (is_wp_error($user) && !in_array($user->get_error_code(), $ignore_codes) ) {
        do_action('wp_login_failed', $username);
    }

    return $user;
}
endif;

3. Below function will get execute if the user clicks the activation link in the email.

add_action( 'template_redirect', 'wpse8170_activate_user' );
function wpse8170_activate_user() {
    if ( is_page() && get_the_ID() == /* YOUR ACTIVATION PAGE ID HERE */ ) {
        $user_id = filter_input( INPUT_GET, 'user', FILTER_VALIDATE_INT, array( 'options' => array( 'min_range' => 1 ) ) );
        if ( $user_id ) {
            // get user meta activation hash field
            $code = get_user_meta( $user_id, 'has_to_be_activated', true );
            if ( $code == filter_input( INPUT_GET, 'key' ) ) {
                delete_user_meta( $user_id, 'has_to_be_activated' );
            }
        }
    }
}