The configuration is a little ugly but works similar to most Unix based systems but, assuming "logs" resolves to the IP address of your log server you need to add a line to /vol/vol0/etc/syslog.conf containing the following:
*.* @logs
This will messages from any source on the filer with any severity to the host logs via UDP. You can also get fancier and do stuff like
*.* *.debug@logs
which will send all of the filer's log entries to the log server with the debug priority.
Make sure you can resolve "logs" from the filer. It will accept FQDNs or (I think) IP addresses as well.
Please note that UDP does not provide reliable delivery so if the filer is having issues they may not show up in the logs on your log server and the filer won't tell you.