My web browser opened, and I logged in. I get the message "Tomboy Web Authorisation Successful - Please return to the Tomboy Preferences window and press Save to start synchronising". So I returned to Tomboy to find the window below.
As you can see, it asks me to press save, but the save button is greyed out!
This is a known bug:
In the meantime before it is fixed, you could try the workaround described in comment #16: