I would guess you're using PHP since you're in the MySQL forum, so I would suggest simply making a new table in your database with all the things people have searched for (from the look of your page it looks like you already have that table) and use this code on that table:
$query=mysql_query("SELECT * FROM search_terms_table");
echo mysql_num_rows($query);
replace the "search_terms_table" bit with whatever the table name is and your done
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since Jan 2008