Click on the facebook application, and then
Click on the menu button [with the bb logo'>
Go to "options"
Select "logout"
A pop-up message will come up, say "yes"
It will automatically logout, and will require the password to be re-typed if you want to log in
After the last step, you can also go to the phone's main menu and choose "options" and then "applications" and then filter "add-on" and then delete the facebook application and restart the phone to complete the action IF you want to remove facebook app entirely from your bb instead of just logging out
HTH :)