See for instance http://www.linuxhomenetworking.com/linux-hn/logging.htm
Some notes to go with that:
On the host that *receives* logs:
- check if you need to separate logs by IP or name or use TCP instead of UDP (replace Syslogd with Syslog-NG or RSyslog),
- check if you need more secure logging over SSL (install Stunnel on both sides),
- check 'man syslogd' for needing '-l' or '-s',
- check your firewall contains an appropriate line for host(s) allowed access to syslogd ('getent services syslog'),
- check your /etc/hosts.deny contains the 'ALL: ALL' line if you need strict access controls,
- check your /etc/hosts.allow contains an appropriate line for host(s) allowed access to syslogd.
On the host that *sends* logs:
- check your firewall contains an appropriate line for outbound access to the syslogd host,
- use 'logger' with an appropriate facility + priority combo to generate a test message or wait aeons for one to show up on the loghost.