Wordpress - Send user activation email when programmatically creating user

To accomplish user activation process you need to do following steps:

1. after create new user add a custom user field which indicates that this user has to activate his account
2. send an email with activation code, provide a link in this email to a page where user will be activated
3. implement activation page
4. when user attempts to log in check if that custom user field exists or not. If it exists then do not log him in and show activation error message instead.

Add custom field and send email:

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', 'CONGRATS BLA BLA BLA. HERE IS YOUR ACTIVATION LINK: ' . $activation_link );
    }
}

Check user activation on login:

// 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;

Activation page:

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' );
            }
        }
    }
}

This is your starting point, go ahead and adjust it for your needs.