Once you have the current session up and running, choose the File drop-down and select Save Session As...
This will allow you to save a copy of just the session. This is only a copy of the session and not a copy of all the audio/fade files. So don't worry.
When saving the different versions, name them appropriately. The last thing you want is to give it some ridiculous name that is impossible to locate in a search.
I like to save them specific to the task at hand. For instance, if I'm adding background vocals to a chorus I may notate it like this: "_________ BV Vox Chorus."
Some people like to label them specific to the day the work was done.
Make sure that the alternate session icon is saved to the same song folder as the original. You don't want to have multiple files all over your computer. They should exist inside the original folder to ensure posterity.
After you've amassed a vast amount of these alternate sessions you may want to create a folder within the original session folder and name it "Previous Session." This way you can put all the older versions of the song into this folder while leaving the current session readily available.