This ought to work for Airport Express devices too, although I’ve not tested it. Ditto it should be similar on a BSD like machine.

On your debian / ubuntu box

• If you have a firewall / iptables setup, enable UDP port 514 from your local network (or at least the IP of the Airport)

• Add the following line to /etc/syslog.conf

  local0.* /var/log/AirPort.log

• To prevent the Airport messages also appearing in /var/log/messages, find the stanza in /etc/syslog.conf that controls that file and add

  !local0.*;\

• Restart your syslog deamon

  sudo /etc/init.d/sysklogd restart

Access the Airport via your Airport Utility

• Advanced tab
• Syslog Destination Address is the IP or hostname of the Debian / Ubuntu linux box that you want to contain the logs. Start with the IP address to get it working, then flip to a hostname if you prefer.

See also AirPort Extreme: Remotely logging base station activity