Files I wrote on my desktop using 12.04 with Libreoffice and saved in Word format are in my Ubuntu One folder. I thought I could edit them away from home, as I do on Sky Drive. But when I opened one it only downloaded it to my laptop (which is using 11.10 and Abiword). Do I have to edit the file and then upload it back to the cloud? Will it then replace the original?
Short answer: Yes, no and yes.
Slightly longer: Ubuntu One provides only a storage cloud, no editing tools.
I just realized that you probably didn't add your notebook as a device to UbuntuOne and so no automatical syncing will take place at all. So that would need to be done first.
Then if you edit the file on your notebook and save it it should get automatically synced back to UbuntuOne and then to your other system. (This doesn't apply for a smartphone, UbuntuOne Files for Android provide only downloading the files).