Adding a Pinch of Salt

Following the recent LinkedIn breach, the company has stated that their current production database contains salted passwords. Obviously this was not the case at the time of the breach (SHA1, unsalted), so a salt value must have been added to improve security. But how can you add a salt value to a password hash, if you don't know the password?

Firstly, let's consider the difference between a salted and unsalted password hash: