This approach works for any linux operating system, including Ubuntu, and is probably most often used in conjunction with web development work.
tail -f /path/thefile.log
This will give you a scrolling view of the logfile. As new lines are added to the end, they will show up in your console screen.
For Ruby on Rails, for instance, you can view the development logfile by running the command from your project directory:
tail -f log/development.log
As with all linux apps, Ctrl+C will stop it.