I am trying to edit and debug an existing linux-based Apache2 web site, to no success. When I create a project I am forced to declare the root directory, but the directory is of course on /var/www at the remote machines, for which I have the root password.
I know it can be done, but how exactly I edit a remote site without a network mapping of drives of any sort?
I tried copying all files and creating a local copy of /var/www, but it fails to run because it checks for some libraries and they are not here, the graphic libraries. The remote system is Debian 7.0. So how do I do this?

Still you can select /var/www as root directory
What you need is SSH/SFTP account for this server -- it means that you will access it with username/password or username/public key.
Account can be created in Tools->Accounts.
Then you can test it in View->Tabs->Explorer window.
Then open project properties, click on the rightmost button in the root directory input, expand ssh account in the directory tree and select /var/www. It will look like [accountname] /var/www

You don't need root password, just a regular user that has write permissions for the web tree (/var/www in your case) will be enough.