Check if Website is hidden from Search Engines?

Using this since Milos answer on every WordPress project as a handy snippet (put it right after the opening body tag):

<?php if ( is_user_logged_in() ) { ?>
    <style>
        a.searchengines_blocked {
            position: fixed;
            bottom: 0;
            left: 0;
            z-index: 99999;
            color: black !important;
            background-color: #ffcd1b !important;
            font-weight: normal;
            font-size: 1.8rem;
            padding: 6px 15px;
            text-align: center;
            vertical-align: middle;
            border-top-right-radius: 10px;
        }
    </style>
    <?php
        if( 0 == get_option( 'blog_public' ) ){
            echo '<a href="./wp-admin/options-reading.php" class="searchengines_blocked">!G</a>';
        }
    ?>
<?php } ?>

Another way to see if your Website is hidden from Search Engines is going to Settings » Privacy Settings

The Site Privacy setting controls who can view your site, allowing you to make the site private or public. To access this setting, go to My Site → Settings and look for Privacy.

Privacy Options

1. Public: This is the setting used by most sites. It allows everyone to read your site and enables your site to be included in search engine results and other content sites.

2. Hidden: If you want all human visitors to be able to read your blog, but want to block web crawlers for search engines, this is the setting for you. (Please note, however, that not all search engines respect this setting.)

3. Private: Select this option to make your site private. If you want specific people to be able to view it (and add comments, if you’ve enabled them), you’ll need to invite them to be a viewer.

Pretty sure I stole borrowed the following piece of code from the very handy and useful Yoast Plugin:

/**
 * Check if Website is visible to Search Engines
 */
function wpse_check_visibility() {
    if ( ! class_exists( 'WPSEO_Admin' ) ) {
        if ( '0' == get_option( 'blog_public' ) ) {
            add_action( 'admin_footer', 'wpse_private_wp_warning' );
        }
    }
}
add_action( 'admin_init', 'wpse_check_visibility' );

/**
 * If website is Private, show alert
 */
function wpse_private_wp_warning() {
    if ( ( function_exists( 'is_network_admin' ) && is_network_admin() ) ) {
        return;
    }

    echo '<div id="robotsmessage" class="error">';
    echo '<p><strong>' . __( 'Huge SEO Issue: You\'re blocking access to robots.', 'wpse-seo' ) . '</strong> ' . sprintf( __( 'You must %sgo to your Reading Settings%s and uncheck the box for Search Engine Visibility.', 'wordpress-seo' ), '<a href="' . esc_url( admin_url( 'options-reading.php' ) ) . '">', '</a>' ) . '</p></div>';
}

Pretty much on admin_init we check if our site is private. If it is we're going to use the footer and WordPress alert styles to tell us that the site is private. The WPSEO_Admin is Yoast as I believe they will also tell you the site is private if it's installed so we don't want to step on their toes.

The setting is stored in the option blog_public.

if( 0 == get_option( 'blog_public' ) ){
    echo 'search engines discouraged';
}