We advise that you do a full backup of your Joomla site before even thinking about this!

  1. Go to your global configuration and search for the database
  2. Change your database prefix (Example: new_) and press Save.
  3. Go to phpMyAdmin to access your database, from the Cpanel.
  4. Go to export, leave all default values and press Start. Exporting the database can take a while.
  5. When done, select all code and copy it to notepad (or any other text editor)
  6. In phpMyAdmin, select all tables and delete them
  7. In notepad, do a Search & replace (Ctrl + H). Set the searchterm to jos_ and change it into your new prefix (Example: fdasqw_). Press "Replace all".
  8. Select everything in your notepad file and copy it. In phpMyAdmin, go to SQL, paste the queries and press Start.

 

Note: Since Joomla 2.5 the installation creates random prefixes - this workaround is no longer necessary if you are on Joomla 2.5

Source/credits: http://www.marcofolio.net