The following feature does not include getting ready for the new time period.
If you are looking for info on how to recreate your classes in a new season, you can find out here.

The following info is just if you wanted to move a current class to another season because the dates have changed or you want to make an amendment to a mistake.

To move a class between seasons first head to the class page, and click Copy Class.

It will then open the page as shown below where you can select the new season on the dropdown.

If you have already billed for this class in the former season you have moved it from, you will not be able to bill for it after you have moved it into the new season. Once a class has been billed for, the system will know that and it will not generate any further invoices for it.
If you are looking to bill again you will need to use the 'Clone' feature. Find out how to do this here