You can give a puzzle a name, or save under a new name by selecting Save As... from the File menu. Enter the name for the puzzle and press OK. You can select a different folder or save to a different disk as you like.
You can save a puzzle with its current name by pressing Ctrl+S or selecting Save from the File menu.
To save in old Crossword Compiler 4/5 format select the option from the Save as Type drop-down box. Otherwise, the file will require Crossword Compiler 6 or higher to be opened. Of course if you use features introduced in a particular version they will not be available if opened in an older version.
To save a puzzle for use with other programs use the Export feature.