How can I make an auto-fill search box auto-completing with the tags?

First:
I love Greek. Studied it recently – it is fun to see a site in Greek!

Second:
Your site is loading in excess of 25 script files. That is NOT helping your site load times. You should consider reducing this if at all possible.

And now, the answer to your question:
You are using the Simple Instant Search Plugin, which works by using a shortcode [IS].
The instant search isn’t working on the page you pointed me to because it does not use the shortcode, but rather uses the standard WordPress search box. The plugin you are using does not affect the built-in search, but relies on the use of their shortcode. Please refer to The plugin’s FAQ to see how to make the search work.

Finally, if you want the instant search to be used everywhere the WordPress search form is displayed, then you need to follow a slightly different path:

  1. Find your theme’s searchform.php file
  2. Edit the file and use the php snippet from The plugin’s FAQ. Basically, you would replace the built-in form elements with the following code:
    <?php echo do_shortcode('[IS]'); ?>

If your theme does not contain a searchform.php file yet, that’s OK – they are quite simple. Just create a file, name it searchform.php, and edit it. Place the following code into it:

<form id="searchform" method="get" action="<?php echo home_url( "https://wordpress.stackexchange.com/" ); ?>">
    <div> 
        <input type="text" name="s" id="s" class="searchfield" size="15" /><input class="searchbutton" type="submit" value="Search" />
    </div>
</form>

Save, and that’s a typical looking searchform file.

Of course, in order to accomplish what you want, you would create the searchform.php file, and paste just this into it:

<?php echo do_shortcode('[IS]'); ?>

Hope that helps!