If your ILIAS is already istalled, the apache webserver is active, too. If apache isn't installed for any reason, do so:

apt-get install apache2

To test the kerberos configuration, php5 and phpinfo will be helpful.

Apache needs a module for kerberos authentication:

apt-get install libapache2-mod-auth-kerb

The installation of mod_auth_kerb may have activated the module, else this has to be done now and Apache must be restarted/reloaded.

a2enmod headers
service apache2 restart

The Kerberos module offers authentication by password (The user is presented a window to enter username and password) oder negotiation (webserver and user-session on the client authenticate to Kerberos and tickets are apssed). Negotiation as method offers a direct login to the ILIAS server ("single sign on") and doesn't pass the user's password to the ILIAS service, which enhances security.
The following configurations thus disable the basic authentication method. As a fallback method for logging in with non-kerberos clients, any other login method can be used, e.g. LDAP or ILIAS database.