If you wish to log to the console, you can use the logging console command.
This table shows you the levels of logging available:
<0-7> Enter syslog level (0 - 7)
WORD Specify the name of logging list
alerts Immediate action needed (severity=1)
critical Critical conditions (severity=2)
debugging Debugging messages (severity=7)
emergencies System is unusable (severity=0)
errors Error conditions (severity=3)
informational Informational messages (severity=6)
notifications Normal but significant conditions (severity=5)
warnings Warning conditions (severity=4)
If you wish to use a syslog server, the very excellent visual syslog is free and open source, and works well. http://maxbelkov.github.io/visualsyslog/
It uses the default port 514
From the config prompt, use the logging host command.
Use logging trap to set the level. If you use level 7, you will find ASA is too verbose.