Log files for Magento are found within the /var/log directory.
By default there are two files, exception.log and system.log
If you're trying to debug an issue that you're having one of the best places to start is in the exception.log
If your log files are empty this will mean that either the files don't have the correct permissions (they should be 777) or logging isn't enabled.
To enable system and exception logging you'll need to login to the Admin.
Once there, go to
System > Configuration > Developer > Log Settings and then set Enabled to Yes.
Simple as that, happy coding!