The two most popular syslog deamons (the programs that run in the background to accept and write or forward logs) are rsyslog and syslog-ng. One of these will most likely be running on your Linux distribution.
Please refer to the documentation of your distribution if you are not sure about this.
These instructions configure rsyslog and syslog-ng to send log messages unencrypted over the network. This is generally not recommended on public networks.