For anyone with an Ubuntu One account, the following are instructions for sending invites:
Go to My Files in the web interface.
Create a new folder (to be shared) with the person that you will be inviting
Go to the sharing tab (on the right).
Share the folder with the person that you want to invite (The trick is that someone does not have to have an Ubuntu One account to accept a share).
For anyone looking for an invite, just ask @bugabundo at Identi.ca