When connected to Ubuntu one via an internet browser, how do I move files between my different folders in Ubuntu One?
There's no way to move the files between folders in Ubuntu One web interface, you can just Publish, Download or Delete them.
Here is how I managed to move files between folders:
1/ open ubuntuone on PC and on U1 webpage
2/ on the U1 webpage, create the folder you want (eg "shared")
3/ open your U1 folder on your PC, and you should see the new folder (eg "shared")
4/ on your PC, copy file from your U1 folder to "shared" folder.
5/ on your U1 webpage, you should now see the copied files in your "shared" folder.