<?php
include("config.php");
$data = array();
 
$data [] = 'firma';
$data [] = 'adress';
$data [] = 'tel';
 
    if (isset($_POST['vvod'])) {
        $firma = $_POST['firma'];
        $adress = $_POST['adress'];
        $tel = $_POST['tel'];
   
        if ($firma != '' and $adress != '' and $tel != '') {
         $proadd = mysql_query("SELECT * FROM `clients` WHERE `firma` = '".$firma."'");
            if(mysql_num_rows($proadd) > 0){
            ?> <script> alert('Такой клиент уже есть в базе!'); </script><?
			
            }
            else{
            $add = mysql_query("INSERT INTO clients(firma,adress,tel) VALUES ('$firma','$adress','$tel')");
            header("Location: ".$_SERVER['REQUEST_URI']);
            }
}
else
{
    echo "Вы заполнили не все поля";
}
}
?>

select * from your_db where lower(your_table_for_select) like '%string%'

$var = mb_strtolower($var, 'UTF-8');
$proadd = mysql_query("SELECT * FROM `clients` WHERE lower(`firma`) = '".$var."'");