How can I create a new folder in Word for Mac ?

Select Open in Word's File menu. At the bottom left of the dialog should be an option for a New Folder. Optionally, you can create a new folder outside of Word. Go to the location where you want the new folder, then press COMMAND-SHIFT-N and a new folder titled "untitled folder" will appear.

Select the files you want to move and click on COMMAND-C to copy. Go to the new folder and open it in the Finder, then press COMMAND-V to paste. If you don't want the copied files in the source folder then return to it and drag the selected files to the Trash.

You don't do this in Word. You do it in the OS X Finder.

All you need do in Word is open the file, then select Save As from Word's File menu. Change the destination to your new folder then click on the Save button.

The Finder method is much faster if you have a number of files you want to move. Just remember that to open those moved files in Word, you will have to change the directory from which you will open those files.