Because passwords are stored using a one-way MD5 hash which prevents recovering the password, you cannot recover an existing password, but you can reset it to a new password by editing the password field in the database. In the following directions, you will set the password MD5 value to a known value and then log-in using the password that matches that value. Once logged in, you can change the password again using normal Joomla! user access screens.
Joomla! 1.0.13 Enhanced Password System
Initial tests indicate that the method described here also works with Joomla! 1.0.13 salt-enhanced passwords. This is because Joomla! automatically updates password data from earlier versions to the 1.0.13 format.