How can one start a process and monitor its syslog messages?
Using the tail command in Terminal.app will follow a log file and print out in real time whats being written to just that log file.

tail -f /path/to/your/log/file.log


If your process has a common name that shows in every log file, like com.my.process you can tail the file and grep out for that keyword/process.

tail -f /var/log/system.log | grep "com.my.process"


tail command