Create an Alias in the apache config, like:
Alias /observium /opt/observium/html


Set the base_url in config.php:
$config['base_url'] = "http://www.example.com/observium/";
The trailing / is required!


Set the rewrite-base in html/.htaccess:
RewriteBase /observium/
The trailing / is required!


Change the following line in html/index.php:
$segments = explode('/', trim($_SERVER['REQUEST_URI'], '/'));
to:
$segments = explode('/', trim($_SERVER['PATH_INFO'], '/'));