Say you have downloaded a torrent and want to copy a file from one location to another (for example, from home to friend's house). One simple way of doing this is to use the existing 'Sharing' system within Vuze by creating a 'Personal Share'. Right-click on the torrent, or one of the files in the Files-View, and select 'Personal Share'. This will create a separate torrent for the file (you'll see it in your Library) tracked via the DHT (by default). You can then right click on this new torrent and copy the Magnet-URI for it. Send this URI to your friend and they can add it to their Vuze to download the file.
Of course you will need to continue seeding the torrent until the transfer is complete. You might want to 'Force Start' it to ensure it is running - this is a right-click option for users who have set their 'Mode' (see config settings) to something other than 'Beginner'.
Once completed you can delete the share from 'My Shares' view.
One aspect of a 'Personal Share' that isn't present if you use the File->Share menu (or drag-drop files to the 'My Shares' view) is that the torrent created is guaranteed to be unique so if others don't have access to the URI they can't download it (hence the addition of 'Personal')
Note that you can continue to seed the original download while running a separate Personal Share on it or any of its files.
You might want to consider using the Friends feature to share the torrents as well.