To harden a Unix web server, administrators should (1) install all security patches, (2) disable unnecessary services, (3) monitor system and log files for changes or intrusions, and (4) regularly backup essential files. When configuring a firewall, rules should be established to allow necessary outgoing traffic like HTTP and FTP, while blocking all other traffic and unauthorized incoming traffic. Firewalls can be implemented using a dual-home or screened-host configuration to control access between internal and external networks.