As most of the public HOWTOs seem to be either incomplete or a bit outdated and because I have no copy of the book Advanced Programming in the UNIX Environment, Instead I found the following microHOWTOs:

By following the steps, described there I was able to turn m3player into a daemon. The daemon behavior can be turned on by passing the -d or --daemon switches to the command line. When the daemon switch is specified, all output (stdout and stderr) gets redirected into the log file at the default location /var/log/m3player.log or to the location, specified by the -l or --logfile switch.