不了解涉及查询字符串参数的重写规则

Question

My menu links to internal sites via

<a href="<?php $PHP_SELF ?>?site=company">

index.php includes the content in this way:

if ($_GET['site']=="company") {
    include'sites/company.php';
}

So far so good. Now I searched for hours and tried a lot of stuff to rewrite the address from /index.php?site=company to /company. Nothing takes effect. One of the attempts:

RewriteEngine On
RewriteCond %{REQUEST_FILENAME} !-f
RewriteRule ^([\w]+)/?([\w]+)? /index.php?site=$1

Can anybody help, please? I´m new to .htaccess.