The answer, you don't. You will need to set a password in order to authenticate to do anything requiring authentication.
Unfortunately after the password has been removed you cannot even change your password as you must be able to authenticate in order to change your password in the settings / user account screen.
The fix:
Change your password using Terminal.
Click the windows key or click the dash button to go to the dashboard. In the search box type term
and click on the program called terminal
.
Type who am i
and press enter to verify you are logged in as the user that you want to change.
Type passwd
and press enter. It will then ask you what password you want to change it to. Enter your new password and press enter. Then it will ask you to enter your password again to verify. Enter your password again and then press enter. Your password will now be set and you will now be able to authenticate again by using your new password.