There are entirely too many options.
I use Tony's method. I actually backup the course as many times as parts that I want. I select just the Lessons I want for the new course when I do the backup and change the name of the backup to make it obvious which is which. This is easier than deleting courses from the same course restored for each of the parts. I have learned to leave the original in place for a bit (hide it) and not to use it as a new course.
I think there is also the import function which is available in 1.8 also in the Admin block. This allows the teacher to go to another course they teach and bring in modules and resources. But I use Tony's method.
Hope this helps you and others
Best Chris