In my application, I want to enable logging for debug purposes. I have already inserted several logging statements. However, where can I see these log messages ? How can I output something on the screen ?

After making changes to logger.conf make sure you go in to the asterisk CLI and type in logger reload. The default location for the logs is /var/log/asterisk. If you wanted to see an ongoing trace of whats going on (which is what I do) try running tail -f /var/log/asterisk/full (if you have full to trace in logger.conf). As things are inserted in to the file they will scroll up on your screen.