<form action="script.php" method="post">
<input type="text" name="jmeno">
<input type="submit" name="submit" value="Odeslat">

</form>

// script.php

<?PHP

if (isset($_POST['submit']) && $_POST['submit']=="Odeslat")
{
  $pripojeni = mysql_connect("localhost","root","lamalama","databases");
  mysql_query("INSERT INTO test (jmeno) VALUES ('".mysql_real_escape_string($_GET["jmeno"])."')",$pripojeni);
  mysql_close($pripojeni);
}

?>